Basic Math Examples

$\frac{3}{2} \cdot \frac{9 - \sqrt{17}}{4} \cdot \frac{9 + \sqrt{17}}{4}$

Step 1

Multiply $\frac{3}{2} \cdot \frac{9 - \sqrt{17}}{4}$ .

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Step 1.1

Multiply $\frac{3}{2}$ by $\frac{9 - \sqrt{17}}{4}$ .

$\frac{3 (9 - \sqrt{17})}{2 \cdot 4} \cdot \frac{9 + \sqrt{17}}{4}$

Step 1.2

Multiply $2$ by $4$ .

$\frac{3 (9 - \sqrt{17})}{8} \cdot \frac{9 + \sqrt{17}}{4}$

Step 2

Multiply $\frac{3 (9 - \sqrt{17})}{8} \cdot \frac{9 + \sqrt{17}}{4}$ .

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Step 2.1

Multiply $\frac{3 (9 - \sqrt{17})}{8}$ by $\frac{9 + \sqrt{17}}{4}$ .

$\frac{3 (9 - \sqrt{17}) (9 + \sqrt{17})}{8 \cdot 4}$

Step 2.2

Multiply $8$ by $4$ .

$\frac{3 (9 - \sqrt{17}) (9 + \sqrt{17})}{32}$

Step 3

Simplify the numerator.

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Step 3.1

Apply the distributive property.

$\frac{(3 \cdot 9 + 3 (- \sqrt{17})) (9 + \sqrt{17})}{32}$

Step 3.2

Multiply $3$ by $9$ .

$\frac{(27 + 3 (- \sqrt{17})) (9 + \sqrt{17})}{32}$

Step 3.3

Multiply $- 1$ by $3$ .

$\frac{(27 - 3 \sqrt{17}) (9 + \sqrt{17})}{32}$

Step 3.4

Expand $(27 - 3 \sqrt{17}) (9 + \sqrt{17})$ using the FOIL Method.

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Step 3.4.1

Apply the distributive property.

$\frac{27 (9 + \sqrt{17}) - 3 \sqrt{17} (9 + \sqrt{17})}{32}$

Step 3.4.2

Apply the distributive property.

$\frac{27 \cdot 9 + 27 \sqrt{17} - 3 \sqrt{17} (9 + \sqrt{17})}{32}$

Step 3.4.3

Apply the distributive property.

$\frac{27 \cdot 9 + 27 \sqrt{17} - 3 \sqrt{17} \cdot 9 - 3 \sqrt{17} \sqrt{17}}{32}$

Step 3.5

Simplify and combine like terms.

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Step 3.5.1

Simplify each term.

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Step 3.5.1.1

Multiply $27$ by $9$ .

$\frac{243 + 27 \sqrt{17} - 3 \sqrt{17} \cdot 9 - 3 \sqrt{17} \sqrt{17}}{32}$

Step 3.5.1.2

Multiply $9$ by $- 3$ .

$\frac{243 + 27 \sqrt{17} - 27 \sqrt{17} - 3 \sqrt{17} \sqrt{17}}{32}$

Step 3.5.1.3

Multiply $- 3 \sqrt{17} \sqrt{17}$ .

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Step 3.5.1.3.1

Raise $\sqrt{17}$ to the power of $1$ .

$\frac{243 + 27 \sqrt{17} - 27 \sqrt{17} - 3 ({\sqrt{17}}^{1} \sqrt{17})}{32}$

Step 3.5.1.3.2

Raise $\sqrt{17}$ to the power of $1$ .

$\frac{243 + 27 \sqrt{17} - 27 \sqrt{17} - 3 ({\sqrt{17}}^{1} {\sqrt{17}}^{1})}{32}$

Step 3.5.1.3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{243 + 27 \sqrt{17} - 27 \sqrt{17} - 3 {\sqrt{17}}^{1 + 1}}{32}$

Step 3.5.1.3.4

Add $1$ and $1$ .

$\frac{243 + 27 \sqrt{17} - 27 \sqrt{17} - 3 {\sqrt{17}}^{2}}{32}$

Step 3.5.1.4

Rewrite ${\sqrt{17}}^{2}$ as $17$ .

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Step 3.5.1.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{17}$ as $17^{\frac{1}{2}}$ .

$\frac{243 + 27 \sqrt{17} - 27 \sqrt{17} - 3 {(17^{\frac{1}{2}})}^{2}}{32}$

Step 3.5.1.4.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{243 + 27 \sqrt{17} - 27 \sqrt{17} - 3 \cdot 17^{\frac{1}{2} \cdot 2}}{32}$

Step 3.5.1.4.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{243 + 27 \sqrt{17} - 27 \sqrt{17} - 3 \cdot 17^{\frac{2}{2}}}{32}$

Step 3.5.1.4.4

Cancel the common factor of $2$ .

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Step 3.5.1.4.4.1

Cancel the common factor.

$\frac{243 + 27 \sqrt{17} - 27 \sqrt{17} - 3 \cdot 17^{\frac{2}{2}}}{32}$

Step 3.5.1.4.4.2

Rewrite the expression.

$\frac{243 + 27 \sqrt{17} - 27 \sqrt{17} - 3 \cdot 17^{1}}{32}$

Step 3.5.1.4.5

Evaluate the exponent.

$\frac{243 + 27 \sqrt{17} - 27 \sqrt{17} - 3 \cdot 17}{32}$

Step 3.5.1.5

Multiply $- 3$ by $17$ .

$\frac{243 + 27 \sqrt{17} - 27 \sqrt{17} - 51}{32}$

Step 3.5.2

Subtract $51$ from $243$ .

$\frac{192 + 27 \sqrt{17} - 27 \sqrt{17}}{32}$

Step 3.5.3

Subtract $27 \sqrt{17}$ from $27 \sqrt{17}$ .

$\frac{192 + 0}{32}$

Step 3.5.4

Add $192$ and $0$ .

$\frac{192}{32}$

Step 4

Divide $192$ by $32$ .

$6$