الجبر الخطي الأمثلة

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

خطوة 1

اضرب $\frac{1}{\sqrt{2}}$ في $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

خطوة 2

جمّع وبسّط القاسم.

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خطوة 2.1

اضرب $\frac{1}{\sqrt{2}}$ في $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

خطوة 2.2

ارفع $\sqrt{2}$ إلى القوة $1$ .

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

خطوة 2.3

ارفع $\sqrt{2}$ إلى القوة $1$ .

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

خطوة 2.4

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 2.5

أضف $1$ و $1$ .

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

خطوة 2.6

أعِد كتابة ${\sqrt{2}}^{2}$ بالصيغة $2$ .

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خطوة 2.6.1

استخدِم $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ لكتابة $\sqrt{2}$ في صورة $2^{\frac{1}{2}}$ .

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

خطوة 2.6.2

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

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

خطوة 2.6.3

اجمع $\frac{1}{2}$ و $2$ .

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

خطوة 2.6.4

ألغِ العامل المشترك لـ $2$ .

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خطوة 2.6.4.1

ألغِ العامل المشترك.

خطوة 2.6.4.2

أعِد كتابة العبارة.

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

خطوة 2.6.5

احسِب قيمة الأُس.

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

خطوة 3

اضرب بسط الكسر في مقلوب القاسم.

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

خطوة 4

ألغِ العامل المشترك لـ $0.5$ .

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خطوة 4.1

أخرِج العامل $0.5$ من $2$ .

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

خطوة 4.2

ألغِ العامل المشترك.

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

خطوة 4.3

أعِد كتابة العبارة.

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

خطوة 5

اضرب $\frac{1}{\sqrt{3}}$ في $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

خطوة 6

جمّع وبسّط القاسم.

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خطوة 6.1

اضرب $\frac{1}{\sqrt{3}}$ في $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

خطوة 6.2

ارفع $\sqrt{3}$ إلى القوة $1$ .

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

خطوة 6.3

ارفع $\sqrt{3}$ إلى القوة $1$ .

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

خطوة 6.4

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 6.5

أضف $1$ و $1$ .

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

خطوة 6.6

أعِد كتابة ${\sqrt{3}}^{2}$ بالصيغة $3$ .

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خطوة 6.6.1

استخدِم $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ لكتابة $\sqrt{3}$ في صورة $3^{\frac{1}{2}}$ .

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

خطوة 6.6.2

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

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

خطوة 6.6.3

اجمع $\frac{1}{2}$ و $2$ .

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

خطوة 6.6.4

ألغِ العامل المشترك لـ $2$ .

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خطوة 6.6.4.1

ألغِ العامل المشترك.

خطوة 6.6.4.2

أعِد كتابة العبارة.

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

خطوة 6.6.5

احسِب قيمة الأُس.

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

خطوة 7

اضرب $\frac{1}{\sqrt{2}}$ في $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

خطوة 8

جمّع وبسّط القاسم.

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خطوة 8.1

اضرب $\frac{1}{\sqrt{2}}$ في $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

خطوة 8.2

ارفع $\sqrt{2}$ إلى القوة $1$ .

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

خطوة 8.3

ارفع $\sqrt{2}$ إلى القوة $1$ .

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

خطوة 8.4

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 8.5

أضف $1$ و $1$ .

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

خطوة 8.6

أعِد كتابة ${\sqrt{2}}^{2}$ بالصيغة $2$ .

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خطوة 8.6.1

استخدِم $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ لكتابة $\sqrt{2}$ في صورة $2^{\frac{1}{2}}$ .

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

خطوة 8.6.2

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

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

خطوة 8.6.3

اجمع $\frac{1}{2}$ و $2$ .

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

خطوة 8.6.4

ألغِ العامل المشترك لـ $2$ .

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خطوة 8.6.4.1

ألغِ العامل المشترك.

خطوة 8.6.4.2

أعِد كتابة العبارة.

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

خطوة 8.6.5

احسِب قيمة الأُس.

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

خطوة 9

اضرب بسط الكسر في مقلوب القاسم.

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

خطوة 10

ألغِ العامل المشترك لـ $0.5$ .

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خطوة 10.1

أخرِج العامل $0.5$ من $2$ .

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

خطوة 10.2

ألغِ العامل المشترك.

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

خطوة 10.3

أعِد كتابة العبارة.

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

خطوة 11

اضرب $\frac{1}{\sqrt{3}}$ في $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

خطوة 12

جمّع وبسّط القاسم.

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خطوة 12.1

اضرب $\frac{1}{\sqrt{3}}$ في $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

خطوة 12.2

ارفع $\sqrt{3}$ إلى القوة $1$ .

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

خطوة 12.3

ارفع $\sqrt{3}$ إلى القوة $1$ .

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

خطوة 12.4

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 12.5

أضف $1$ و $1$ .

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

خطوة 12.6

أعِد كتابة ${\sqrt{3}}^{2}$ بالصيغة $3$ .

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خطوة 12.6.1

استخدِم $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ لكتابة $\sqrt{3}$ في صورة $3^{\frac{1}{2}}$ .

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

خطوة 12.6.2

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

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

خطوة 12.6.3

اجمع $\frac{1}{2}$ و $2$ .

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

خطوة 12.6.4

ألغِ العامل المشترك لـ $2$ .

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خطوة 12.6.4.1

ألغِ العامل المشترك.

خطوة 12.6.4.2

أعِد كتابة العبارة.

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

خطوة 12.6.5

احسِب قيمة الأُس.

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

خطوة 13

اضرب $\frac{1}{\sqrt{1.5}}$ في $\frac{\sqrt{1.5}}{\sqrt{1.5}}$ .

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

خطوة 14

جمّع وبسّط القاسم.

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خطوة 14.1

اضرب $\frac{1}{\sqrt{1.5}}$ في $\frac{\sqrt{1.5}}{\sqrt{1.5}}$ .

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

خطوة 14.2

ارفع $\sqrt{1.5}$ إلى القوة $1$ .

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

خطوة 14.3

ارفع $\sqrt{1.5}$ إلى القوة $1$ .

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

خطوة 14.4

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 14.5

أضف $1$ و $1$ .

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

خطوة 14.6

أعِد كتابة ${\sqrt{1.5}}^{2}$ بالصيغة $1.5$ .

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خطوة 14.6.1

استخدِم $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ لكتابة $\sqrt{1.5}$ في صورة ${1.5}^{\frac{1}{2}}$ .

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

خطوة 14.6.2

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

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

خطوة 14.6.3

اجمع $\frac{1}{2}$ و $2$ .

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

خطوة 14.6.4

ألغِ العامل المشترك لـ $2$ .

انقر لعرض المزيد من الخطوات...

خطوة 14.6.4.1

ألغِ العامل المشترك.

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

خطوة 14.6.4.2

أعِد كتابة العبارة.

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

خطوة 14.6.5

احسِب قيمة الأُس.

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

خطوة 15

احسِب قيمة الجذر.

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

خطوة 16

اقسِم $1.22474487$ على $1.5$ .

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

خطوة 17

اضرب $\frac{1}{\sqrt{3}}$ في $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

خطوة 18

جمّع وبسّط القاسم.

انقر لعرض المزيد من الخطوات...

خطوة 18.1

اضرب $\frac{1}{\sqrt{3}}$ في $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

خطوة 18.2

ارفع $\sqrt{3}$ إلى القوة $1$ .

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

خطوة 18.3

ارفع $\sqrt{3}$ إلى القوة $1$ .

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

خطوة 18.4

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 18.5

أضف $1$ و $1$ .

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

خطوة 18.6

أعِد كتابة ${\sqrt{3}}^{2}$ بالصيغة $3$ .

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خطوة 18.6.1

استخدِم $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ لكتابة $\sqrt{3}$ في صورة $3^{\frac{1}{2}}$ .

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

خطوة 18.6.2

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

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

خطوة 18.6.3

اجمع $\frac{1}{2}$ و $2$ .

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

خطوة 18.6.4

ألغِ العامل المشترك لـ $2$ .

انقر لعرض المزيد من الخطوات...

خطوة 18.6.4.1

ألغِ العامل المشترك.

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

خطوة 18.6.4.2

أعِد كتابة العبارة.

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

خطوة 18.6.5

احسِب قيمة الأُس.

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

خطوة 19

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

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خطوة 19.1

يمكن ضرب مصفوفتين إذا كان عدد الأعمدة في المصفوفة الأولى يساوي عدد الصفوف في المصفوفة الثانية فقط. في هذه الحالة، المصفوفة الأولى هي $3 \times 3$ والمصفوفة الثانية هي $3 \times 3$ .

خطوة 19.2

اضرب كل صف في المصفوفة الأولى في كل عمود في المصفوفة الثانية.

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

خطوة 19.3

بسّط كل عنصر من عناصر المصفوفة بضرب جميع العبارات.

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

خطوة 20

اضرب $\frac{1}{\sqrt{2}}$ في $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

خطوة 21

جمّع وبسّط القاسم.

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خطوة 21.1

اضرب $\frac{1}{\sqrt{2}}$ في $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

خطوة 21.2

ارفع $\sqrt{2}$ إلى القوة $1$ .

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

خطوة 21.3

ارفع $\sqrt{2}$ إلى القوة $1$ .

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

خطوة 21.4

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 21.5

أضف $1$ و $1$ .

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

خطوة 21.6

أعِد كتابة ${\sqrt{2}}^{2}$ بالصيغة $2$ .

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خطوة 21.6.1

استخدِم $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ لكتابة $\sqrt{2}$ في صورة $2^{\frac{1}{2}}$ .

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

خطوة 21.6.2

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

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

خطوة 21.6.3

اجمع $\frac{1}{2}$ و $2$ .

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

خطوة 21.6.4

ألغِ العامل المشترك لـ $2$ .

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خطوة 21.6.4.1

ألغِ العامل المشترك.

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

خطوة 21.6.4.2

أعِد كتابة العبارة.

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

خطوة 21.6.5

احسِب قيمة الأُس.

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

خطوة 22

اضرب $\frac{1}{\sqrt{2}}$ في $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

خطوة 23

جمّع وبسّط القاسم.

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خطوة 23.1

اضرب $\frac{1}{\sqrt{2}}$ في $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

خطوة 23.2

ارفع $\sqrt{2}$ إلى القوة $1$ .

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

خطوة 23.3

ارفع $\sqrt{2}$ إلى القوة $1$ .

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

خطوة 23.4

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 23.5

أضف $1$ و $1$ .

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

خطوة 23.6

أعِد كتابة ${\sqrt{2}}^{2}$ بالصيغة $2$ .

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خطوة 23.6.1

استخدِم $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ لكتابة $\sqrt{2}$ في صورة $2^{\frac{1}{2}}$ .

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

خطوة 23.6.2

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

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

خطوة 23.6.3

اجمع $\frac{1}{2}$ و $2$ .

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

خطوة 23.6.4

ألغِ العامل المشترك لـ $2$ .

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خطوة 23.6.4.1

ألغِ العامل المشترك.

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

خطوة 23.6.4.2

أعِد كتابة العبارة.

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

خطوة 23.6.5

احسِب قيمة الأُس.

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

خطوة 24

اضرب بسط الكسر في مقلوب القاسم.

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

خطوة 25

ألغِ العامل المشترك لـ $0.5$ .

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خطوة 25.1

أخرِج العامل $0.5$ من $2$ .

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

خطوة 25.2

ألغِ العامل المشترك.

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

خطوة 25.3

أعِد كتابة العبارة.

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

خطوة 26

اضرب بسط الكسر في مقلوب القاسم.

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

خطوة 27

ألغِ العامل المشترك لـ $0.5$ .

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خطوة 27.1

أخرِج العامل $0.5$ من $2$ .

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

خطوة 27.2

ألغِ العامل المشترك.

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

خطوة 27.3

أعِد كتابة العبارة.

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

خطوة 28

اضرب $\frac{1}{\sqrt{1.5}}$ في $\frac{\sqrt{1.5}}{\sqrt{1.5}}$ .

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

خطوة 29

جمّع وبسّط القاسم.

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خطوة 29.1

اضرب $\frac{1}{\sqrt{1.5}}$ في $\frac{\sqrt{1.5}}{\sqrt{1.5}}$ .

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

خطوة 29.2

ارفع $\sqrt{1.5}$ إلى القوة $1$ .

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

خطوة 29.3

ارفع $\sqrt{1.5}$ إلى القوة $1$ .

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

خطوة 29.4

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 29.5

أضف $1$ و $1$ .

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

خطوة 29.6

أعِد كتابة ${\sqrt{1.5}}^{2}$ بالصيغة $1.5$ .

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خطوة 29.6.1

استخدِم $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ لكتابة $\sqrt{1.5}$ في صورة ${1.5}^{\frac{1}{2}}$ .

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

خطوة 29.6.2

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

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

خطوة 29.6.3

اجمع $\frac{1}{2}$ و $2$ .

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

خطوة 29.6.4

ألغِ العامل المشترك لـ $2$ .

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خطوة 29.6.4.1

ألغِ العامل المشترك.

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

خطوة 29.6.4.2

أعِد كتابة العبارة.

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

خطوة 29.6.5

احسِب قيمة الأُس.

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

خطوة 30

احسِب قيمة الجذر.

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

خطوة 31

اقسِم $1.22474487$ على $1.5$ .

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

خطوة 32

اضرب $\frac{1}{\sqrt{3}}$ في $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

خطوة 33

جمّع وبسّط القاسم.

انقر لعرض المزيد من الخطوات...

خطوة 33.1

اضرب $\frac{1}{\sqrt{3}}$ في $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

خطوة 33.2

ارفع $\sqrt{3}$ إلى القوة $1$ .

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

خطوة 33.3

ارفع $\sqrt{3}$ إلى القوة $1$ .

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

خطوة 33.4

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 33.5

أضف $1$ و $1$ .

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

خطوة 33.6

أعِد كتابة ${\sqrt{3}}^{2}$ بالصيغة $3$ .

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خطوة 33.6.1

استخدِم $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ لكتابة $\sqrt{3}$ في صورة $3^{\frac{1}{2}}$ .

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

خطوة 33.6.2

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

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

خطوة 33.6.3

اجمع $\frac{1}{2}$ و $2$ .

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

خطوة 33.6.4

ألغِ العامل المشترك لـ $2$ .

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خطوة 33.6.4.1

ألغِ العامل المشترك.

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

خطوة 33.6.4.2

أعِد كتابة العبارة.

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

خطوة 33.6.5

احسِب قيمة الأُس.

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

خطوة 34

اضرب $\frac{1}{\sqrt{3}}$ في $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

خطوة 35

جمّع وبسّط القاسم.

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خطوة 35.1

اضرب $\frac{1}{\sqrt{3}}$ في $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

خطوة 35.2

ارفع $\sqrt{3}$ إلى القوة $1$ .

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

خطوة 35.3

ارفع $\sqrt{3}$ إلى القوة $1$ .

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

خطوة 35.4

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 35.5

أضف $1$ و $1$ .

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

خطوة 35.6

أعِد كتابة ${\sqrt{3}}^{2}$ بالصيغة $3$ .

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خطوة 35.6.1

استخدِم $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ لكتابة $\sqrt{3}$ في صورة $3^{\frac{1}{2}}$ .

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

خطوة 35.6.2

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

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

خطوة 35.6.3

اجمع $\frac{1}{2}$ و $2$ .

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

خطوة 35.6.4

ألغِ العامل المشترك لـ $2$ .

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خطوة 35.6.4.1

ألغِ العامل المشترك.

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

خطوة 35.6.4.2

أعِد كتابة العبارة.

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

خطوة 35.6.5

احسِب قيمة الأُس.

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

خطوة 36

اضرب $\frac{1}{\sqrt{3}}$ في $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

خطوة 37

جمّع وبسّط القاسم.

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خطوة 37.1

اضرب $\frac{1}{\sqrt{3}}$ في $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

خطوة 37.2

ارفع $\sqrt{3}$ إلى القوة $1$ .

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

خطوة 37.3

ارفع $\sqrt{3}$ إلى القوة $1$ .

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

خطوة 37.4

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

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

خطوة 37.5

أضف $1$ و $1$ .

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

خطوة 37.6

أعِد كتابة ${\sqrt{3}}^{2}$ بالصيغة $3$ .

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خطوة 37.6.1

استخدِم $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ لكتابة $\sqrt{3}$ في صورة $3^{\frac{1}{2}}$ .

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

خطوة 37.6.2

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

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

خطوة 37.6.3

اجمع $\frac{1}{2}$ و $2$ .

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

خطوة 37.6.4

ألغِ العامل المشترك لـ $2$ .

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خطوة 37.6.4.1

ألغِ العامل المشترك.

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

خطوة 37.6.4.2

أعِد كتابة العبارة.

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

خطوة 37.6.5

احسِب قيمة الأُس.

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

خطوة 38

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

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خطوة 38.1

خطوة 38.2

اضرب كل صف في المصفوفة الأولى في كل عمود في المصفوفة الثانية.

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

خطوة 38.3

بسّط كل عنصر من عناصر المصفوفة بضرب جميع العبارات.

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