लीनियर एलजेब्रा उदाहरण

$[\begin{array}{c} - \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 1

$\frac{1}{\sqrt{2}}$ को $\frac{\sqrt{2}}{\sqrt{2}}$ से गुणा करें.

$[\begin{array}{c} - (\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}) & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 2

भाजक को मिलाएं और सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 2.1

$\frac{1}{\sqrt{2}}$ को $\frac{\sqrt{2}}{\sqrt{2}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 2.2

$\sqrt{2}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 2.3

$\sqrt{2}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 2.4

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 2.5

$1$ और $1$ जोड़ें.

$[\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 2.6

${\sqrt{2}}^{2}$ को $2$ के रूप में फिर से लिखें.

और स्टेप्स के लिए टैप करें…

चरण 2.6.1

$\sqrt{2}$ को $2^{\frac{1}{2}}$ के रूप में फिर से लिखने के लिए $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 2.6.2

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 2.6.3

$\frac{1}{2}$ और $2$ को मिलाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 2.6.4

$2$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 2.6.4.1

उभयनिष्ठ गुणनखंड रद्द करें.

चरण 2.6.4.2

व्यंजक को फिर से लिखें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2^{1}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 2.6.5

घातांक का मान ज्ञात करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 3

भाजक के प्रतिलोम से न्यूमेरेटर को गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - (0.5 \frac{\sqrt{1.5}}{2}) & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 4

$0.5$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 4.1

$2$ में से $0.5$ का गुणनखंड करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - (0.5 \frac{\sqrt{1.5}}{0.5 (4)}) & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 4.2

उभयनिष्ठ गुणनखंड रद्द करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - (0.5 \frac{\sqrt{1.5}}{0.5 \cdot 4}) & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 4.3

व्यंजक को फिर से लिखें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 5

$\frac{1}{\sqrt{3}}$ को $\frac{\sqrt{3}}{\sqrt{3}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 6

भाजक को मिलाएं और सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 6.1

$\frac{1}{\sqrt{3}}$ को $\frac{\sqrt{3}}{\sqrt{3}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 6.2

$\sqrt{3}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 6.3

$\sqrt{3}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 6.4

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 6.5

$1$ और $1$ जोड़ें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 6.6

${\sqrt{3}}^{2}$ को $3$ के रूप में फिर से लिखें.

और स्टेप्स के लिए टैप करें…

चरण 6.6.1

$\sqrt{3}$ को $3^{\frac{1}{2}}$ के रूप में फिर से लिखने के लिए $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 6.6.2

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 6.6.3

$\frac{1}{2}$ और $2$ को मिलाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 6.6.4

$2$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 6.6.4.1

उभयनिष्ठ गुणनखंड रद्द करें.

चरण 6.6.4.2

व्यंजक को फिर से लिखें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3^{1}} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 6.6.5

घातांक का मान ज्ञात करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{1}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 7

$\frac{1}{\sqrt{2}}$ को $\frac{\sqrt{2}}{\sqrt{2}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 8

भाजक को मिलाएं और सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 8.1

$\frac{1}{\sqrt{2}}$ को $\frac{\sqrt{2}}{\sqrt{2}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 8.2

$\sqrt{2}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 8.3

$\sqrt{2}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 8.4

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 8.5

$1$ और $1$ जोड़ें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 8.6

${\sqrt{2}}^{2}$ को $2$ के रूप में फिर से लिखें.

और स्टेप्स के लिए टैप करें…

चरण 8.6.1

$\sqrt{2}$ को $2^{\frac{1}{2}}$ के रूप में फिर से लिखने के लिए $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 8.6.2

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 8.6.3

$\frac{1}{2}$ और $2$ को मिलाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2^{\frac{2}{2}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 8.6.4

$2$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 8.6.4.1

उभयनिष्ठ गुणनखंड रद्द करें.

चरण 8.6.4.2

व्यंजक को फिर से लिखें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2^{1}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 8.6.5

घातांक का मान ज्ञात करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 9

भाजक के प्रतिलोम से न्यूमेरेटर को गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - (0.5 \frac{\sqrt{1.5}}{2}) & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 10

$0.5$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 10.1

$2$ में से $0.5$ का गुणनखंड करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - (0.5 \frac{\sqrt{1.5}}{0.5 (4)}) & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 10.2

उभयनिष्ठ गुणनखंड रद्द करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - (0.5 \frac{\sqrt{1.5}}{0.5 \cdot 4}) & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 10.3

व्यंजक को फिर से लिखें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{1}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 11

$\frac{1}{\sqrt{3}}$ को $\frac{\sqrt{3}}{\sqrt{3}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 12

भाजक को मिलाएं और सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 12.1

$\frac{1}{\sqrt{3}}$ को $\frac{\sqrt{3}}{\sqrt{3}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 12.2

$\sqrt{3}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 12.3

$\sqrt{3}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 12.4

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 12.5

$1$ और $1$ जोड़ें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 12.6

${\sqrt{3}}^{2}$ को $3$ के रूप में फिर से लिखें.

और स्टेप्स के लिए टैप करें…

चरण 12.6.1

$\sqrt{3}$ को $3^{\frac{1}{2}}$ के रूप में फिर से लिखने के लिए $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 12.6.2

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 12.6.3

$\frac{1}{2}$ और $2$ को मिलाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 12.6.4

$2$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 12.6.4.1

उभयनिष्ठ गुणनखंड रद्द करें.

चरण 12.6.4.2

व्यंजक को फिर से लिखें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3^{1}} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 12.6.5

घातांक का मान ज्ञात करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{1}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 13

$\frac{1}{\sqrt{1.5}}$ को $\frac{\sqrt{1.5}}{\sqrt{1.5}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{1}{\sqrt{1.5}} \cdot \frac{\sqrt{1.5}}{\sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 14

भाजक को मिलाएं और सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 14.1

$\frac{1}{\sqrt{1.5}}$ को $\frac{\sqrt{1.5}}{\sqrt{1.5}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{\sqrt{1.5} \sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 14.2

$\sqrt{1.5}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{\sqrt{1.5}}^{1} \sqrt{1.5}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 14.3

$\sqrt{1.5}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{\sqrt{1.5}}^{1} {\sqrt{1.5}}^{1}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 14.4

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{\sqrt{1.5}}^{1 + 1}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 14.5

$1$ और $1$ जोड़ें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{\sqrt{1.5}}^{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 14.6

${\sqrt{1.5}}^{2}$ को $1.5$ के रूप में फिर से लिखें.

और स्टेप्स के लिए टैप करें…

चरण 14.6.1

$\sqrt{1.5}$ को ${1.5}^{\frac{1}{2}}$ के रूप में फिर से लिखने के लिए $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{({1.5}^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 14.6.2

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{1.5}^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 14.6.3

$\frac{1}{2}$ और $2$ को मिलाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{1.5}^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 14.6.4

$2$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 14.6.4.1

उभयनिष्ठ गुणनखंड रद्द करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{1.5}^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 14.6.4.2

व्यंजक को फिर से लिखें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{{1.5}^{1}} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 14.6.5

घातांक का मान ज्ञात करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{\sqrt{1.5}}{1.5} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 15

मूलों का मान ज्ञात करें

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & \frac{1.22474487}{1.5} & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 16

$1.22474487$ को $1.5$ से विभाजित करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{1}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 17

$\frac{1}{\sqrt{3}}$ को $\frac{\sqrt{3}}{\sqrt{3}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 18

भाजक को मिलाएं और सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 18.1

$\frac{1}{\sqrt{3}}$ को $\frac{\sqrt{3}}{\sqrt{3}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 18.2

$\sqrt{3}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 18.3

$\sqrt{3}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 18.4

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 18.5

$1$ और $1$ जोड़ें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 18.6

${\sqrt{3}}^{2}$ को $3$ के रूप में फिर से लिखें.

और स्टेप्स के लिए टैप करें…

चरण 18.6.1

$\sqrt{3}$ को $3^{\frac{1}{2}}$ के रूप में फिर से लिखने के लिए $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 18.6.2

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 18.6.3

$\frac{1}{2}$ और $2$ को मिलाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 18.6.4

$2$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 18.6.4.1

उभयनिष्ठ गुणनखंड रद्द करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 18.6.4.2

व्यंजक को फिर से लिखें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{3^{1}} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 18.6.5

घातांक का मान ज्ञात करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{\sqrt{3}}{3} \end{array}] [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 19

और स्टेप्स के लिए टैप करें…

चरण 19.1

दो आव्यूहों को गुणा किया जा सकता है यदि और केवल यदि पहले आव्यूह में स्तंभों की संख्या दूसरे आव्यूह में पंक्तियों की संख्या के बराबर हो. इस स्थिति में, पहला मैट्रिक्स $3 \times 3$ है और दूसरा मैट्रिक्स $3 \times 3$ है.

चरण 19.2

पहले मैट्रिक्स में प्रत्येक पंक्ति को दूसरे मैट्रिक्स में प्रत्येक कॉलम से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} \cdot 1 - \frac{\sqrt{1.5}}{4} \cdot 0 + \frac{\sqrt{3}}{3} \cdot 0 & - \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{1.5}}{4} \cdot 1 + \frac{\sqrt{3}}{3} \cdot 0 & - \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{1.5}}{4} \cdot 0 + \frac{\sqrt{3}}{3} \cdot 4 \\ \frac{\sqrt{2}}{2} \cdot 1 - \frac{\sqrt{1.5}}{4} \cdot 0 + \frac{\sqrt{3}}{3} \cdot 0 & \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{1.5}}{4} \cdot 1 + \frac{\sqrt{3}}{3} \cdot 0 & \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{1.5}}{4} \cdot 0 + \frac{\sqrt{3}}{3} \cdot 4 \\ 0 \cdot 1 + 0.81649658 \cdot 0 + \frac{\sqrt{3}}{3} \cdot 0 & 0 \cdot 0 + 0.81649658 \cdot 1 + \frac{\sqrt{3}}{3} \cdot 0 & 0 \cdot 0 + 0.81649658 \cdot 0 + \frac{\sqrt{3}}{3} \cdot 4 \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 19.3

सभी व्यंजकों को गुणा करके आव्यूह के प्रत्येक अवयव को सरल करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 20

$\frac{1}{\sqrt{2}}$ को $\frac{\sqrt{2}}{\sqrt{2}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - (\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}) & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 21

भाजक को मिलाएं और सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 21.1

$\frac{1}{\sqrt{2}}$ को $\frac{\sqrt{2}}{\sqrt{2}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 21.2

$\sqrt{2}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 21.3

$\sqrt{2}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 21.4

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 21.5

$1$ और $1$ जोड़ें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 21.6

${\sqrt{2}}^{2}$ को $2$ के रूप में फिर से लिखें.

और स्टेप्स के लिए टैप करें…

चरण 21.6.1

$\sqrt{2}$ को $2^{\frac{1}{2}}$ के रूप में फिर से लिखने के लिए $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 21.6.2

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 21.6.3

$\frac{1}{2}$ और $2$ को मिलाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 21.6.4

$2$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 21.6.4.1

उभयनिष्ठ गुणनखंड रद्द करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2^{\frac{2}{2}}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 21.6.4.2

व्यंजक को फिर से लिखें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2^{1}} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 21.6.5

घातांक का मान ज्ञात करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{1}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 22

$\frac{1}{\sqrt{2}}$ को $\frac{\sqrt{2}}{\sqrt{2}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 23

भाजक को मिलाएं और सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 23.1

$\frac{1}{\sqrt{2}}$ को $\frac{\sqrt{2}}{\sqrt{2}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 23.2

$\sqrt{2}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 23.3

$\sqrt{2}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 23.4

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 23.5

$1$ और $1$ जोड़ें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{\sqrt{2}}^{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 23.6

${\sqrt{2}}^{2}$ को $2$ के रूप में फिर से लिखें.

और स्टेप्स के लिए टैप करें…

चरण 23.6.1

$\sqrt{2}$ को $2^{\frac{1}{2}}$ के रूप में फिर से लिखने के लिए $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 23.6.2

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 23.6.3

$\frac{1}{2}$ और $2$ को मिलाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2^{\frac{2}{2}}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 23.6.4

$2$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 23.6.4.1

उभयनिष्ठ गुणनखंड रद्द करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2^{\frac{2}{2}}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 23.6.4.2

व्यंजक को फिर से लिखें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2^{1}} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 23.6.5

घातांक का मान ज्ञात करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 24

भाजक के प्रतिलोम से न्यूमेरेटर को गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - (0.5 \frac{\sqrt{1.5}}{2}) & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 25

$0.5$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 25.1

$2$ में से $0.5$ का गुणनखंड करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - (0.5 \frac{\sqrt{1.5}}{0.5 (4)}) & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 25.2

उभयनिष्ठ गुणनखंड रद्द करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - (0.5 \frac{\sqrt{1.5}}{0.5 \cdot 4}) & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 25.3

व्यंजक को फिर से लिखें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{0.5}{\frac{2}{\sqrt{1.5}}} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 26

भाजक के प्रतिलोम से न्यूमेरेटर को गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - (0.5 \frac{\sqrt{1.5}}{2}) & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 27

$0.5$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 27.1

$2$ में से $0.5$ का गुणनखंड करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - (0.5 \frac{\sqrt{1.5}}{0.5 (4)}) & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 27.2

उभयनिष्ठ गुणनखंड रद्द करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - (0.5 \frac{\sqrt{1.5}}{0.5 \cdot 4}) & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 27.3

व्यंजक को फिर से लिखें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{1}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 28

$\frac{1}{\sqrt{1.5}}$ को $\frac{\sqrt{1.5}}{\sqrt{1.5}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{1}{\sqrt{1.5}} \cdot \frac{\sqrt{1.5}}{\sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 29

भाजक को मिलाएं और सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 29.1

$\frac{1}{\sqrt{1.5}}$ को $\frac{\sqrt{1.5}}{\sqrt{1.5}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{\sqrt{1.5} \sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 29.2

$\sqrt{1.5}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{\sqrt{1.5}}^{1} \sqrt{1.5}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 29.3

$\sqrt{1.5}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{\sqrt{1.5}}^{1} {\sqrt{1.5}}^{1}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 29.4

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{\sqrt{1.5}}^{1 + 1}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 29.5

$1$ और $1$ जोड़ें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{\sqrt{1.5}}^{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 29.6

${\sqrt{1.5}}^{2}$ को $1.5$ के रूप में फिर से लिखें.

और स्टेप्स के लिए टैप करें…

चरण 29.6.1

$\sqrt{1.5}$ को ${1.5}^{\frac{1}{2}}$ के रूप में फिर से लिखने के लिए $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{({1.5}^{\frac{1}{2}})}^{2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 29.6.2

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{1.5}^{\frac{1}{2} \cdot 2}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 29.6.3

$\frac{1}{2}$ और $2$ को मिलाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{1.5}^{\frac{2}{2}}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 29.6.4

$2$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 29.6.4.1

उभयनिष्ठ गुणनखंड रद्द करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{1.5}^{\frac{2}{2}}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 29.6.4.2

व्यंजक को फिर से लिखें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{{1.5}^{1}} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 29.6.5

घातांक का मान ज्ञात करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{\sqrt{1.5}}{1.5} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 30

मूलों का मान ज्ञात करें

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & \frac{1.22474487}{1.5} \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 31

$1.22474487$ को $1.5$ से विभाजित करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 32

$\frac{1}{\sqrt{3}}$ को $\frac{\sqrt{3}}{\sqrt{3}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 33

भाजक को मिलाएं और सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 33.1

$\frac{1}{\sqrt{3}}$ को $\frac{\sqrt{3}}{\sqrt{3}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 33.2

$\sqrt{3}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 33.3

$\sqrt{3}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 33.4

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 33.5

$1$ और $1$ जोड़ें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{{\sqrt{3}}^{2}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 33.6

${\sqrt{3}}^{2}$ को $3$ के रूप में फिर से लिखें.

और स्टेप्स के लिए टैप करें…

चरण 33.6.1

$\sqrt{3}$ को $3^{\frac{1}{2}}$ के रूप में फिर से लिखने के लिए $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 33.6.2

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 33.6.3

$\frac{1}{2}$ और $2$ को मिलाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 33.6.4

$2$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 33.6.4.1

उभयनिष्ठ गुणनखंड रद्द करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 33.6.4.2

व्यंजक को फिर से लिखें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3^{1}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 33.6.5

घातांक का मान ज्ञात करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 34

$\frac{1}{\sqrt{3}}$ को $\frac{\sqrt{3}}{\sqrt{3}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 35

भाजक को मिलाएं और सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 35.1

$\frac{1}{\sqrt{3}}$ को $\frac{\sqrt{3}}{\sqrt{3}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 35.2

$\sqrt{3}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 35.3

$\sqrt{3}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 35.4

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 35.5

$1$ और $1$ जोड़ें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 35.6

${\sqrt{3}}^{2}$ को $3$ के रूप में फिर से लिखें.

और स्टेप्स के लिए टैप करें…

चरण 35.6.1

$\sqrt{3}$ को $3^{\frac{1}{2}}$ के रूप में फिर से लिखने के लिए $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 35.6.2

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 35.6.3

$\frac{1}{2}$ और $2$ को मिलाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 35.6.4

$2$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 35.6.4.1

उभयनिष्ठ गुणनखंड रद्द करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 35.6.4.2

व्यंजक को फिर से लिखें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{1}} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 35.6.5

घातांक का मान ज्ञात करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{1}{\sqrt{3}} \end{array}]$

चरण 36

$\frac{1}{\sqrt{3}}$ को $\frac{\sqrt{3}}{\sqrt{3}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \end{array}]$

चरण 37

भाजक को मिलाएं और सरल करें.

और स्टेप्स के लिए टैप करें…

चरण 37.1

$\frac{1}{\sqrt{3}}$ को $\frac{\sqrt{3}}{\sqrt{3}}$ से गुणा करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}} \end{array}]$

चरण 37.2

$\sqrt{3}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}} \end{array}]$

चरण 37.3

$\sqrt{3}$ को $1$ के घात तक बढ़ाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}} \end{array}]$

चरण 37.4

घातांकों को संयोजित करने के लिए घात नियम $a^{m} a^{n} = a^{m + n}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}} \end{array}]$

चरण 37.5

$1$ और $1$ जोड़ें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{\sqrt{3}}^{2}} \end{array}]$

चरण 37.6

${\sqrt{3}}^{2}$ को $3$ के रूप में फिर से लिखें.

और स्टेप्स के लिए टैप करें…

चरण 37.6.1

$\sqrt{3}$ को $3^{\frac{1}{2}}$ के रूप में फिर से लिखने के लिए $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ का उपयोग करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}} \end{array}]$

चरण 37.6.2

घात नियम लागू करें और घातांक गुणा करें, ${(a^{m})}^{n} = a^{m n}$ .

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}} \end{array}]$

चरण 37.6.3

$\frac{1}{2}$ और $2$ को मिलाएं.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \end{array}]$

चरण 37.6.4

$2$ का उभयनिष्ठ गुणनखंड रद्द करें.

और स्टेप्स के लिए टैप करें…

चरण 37.6.4.1

उभयनिष्ठ गुणनखंड रद्द करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{\frac{2}{2}}} \end{array}]$

चरण 37.6.4.2

व्यंजक को फिर से लिखें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3^{1}} \end{array}]$

चरण 37.6.5

घातांक का मान ज्ञात करें.

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} \end{array}]$

चरण 38

$[\begin{array}{c} - \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} & - \frac{\sqrt{1.5}}{4} & \frac{4 \sqrt{3}}{3} \\ 0 & 0.81649658 & \frac{4 \sqrt{3}}{3} \end{array}] [\begin{array}{c} - \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 0 \\ - \frac{\sqrt{1.5}}{4} & - \frac{\sqrt{1.5}}{4} & 0.81649658 \\ \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} & \frac{\sqrt{3}}{3} \end{array}]$ गुणा करें.

और स्टेप्स के लिए टैप करें…

चरण 38.1

चरण 38.2

$[\begin{array}{c} - \frac{\sqrt{2}}{2} (- \frac{\sqrt{2}}{2}) - \frac{\sqrt{1.5}}{4} (- \frac{\sqrt{1.5}}{4}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & - \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} - \frac{\sqrt{1.5}}{4} (- \frac{\sqrt{1.5}}{4}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & - \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{1.5}}{4} \cdot 0.81649658 + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} \\ \frac{\sqrt{2}}{2} (- \frac{\sqrt{2}}{2}) - \frac{\sqrt{1.5}}{4} (- \frac{\sqrt{1.5}}{4}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} - \frac{\sqrt{1.5}}{4} (- \frac{\sqrt{1.5}}{4}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & \frac{\sqrt{2}}{2} \cdot 0 - \frac{\sqrt{1.5}}{4} \cdot 0.81649658 + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} \\ 0 (- \frac{\sqrt{2}}{2}) + 0.81649658 (- \frac{\sqrt{1.5}}{4}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & 0 \frac{\sqrt{2}}{2} + 0.81649658 (- \frac{\sqrt{1.5}}{4}) + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} & 0 \cdot 0 + 0.81649658 \cdot 0.81649658 + \frac{4 \sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} \end{array}]$

चरण 38.3

सभी व्यंजकों को गुणा करके आव्यूह के प्रत्येक अवयव को सरल करें.

$[\begin{array}{c} 1.92708\overline{3} & 0.92708\overline{3} & 1.08333333 \\ 0.92708\overline{3} & 1.92708\overline{3} & 1.08333333 \\ 1.08333333 & 1.08333333 & 2 \end{array}]$