Evaluate 5/(2 square root of 66)

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Trigonometry

$\frac{5}{2 \sqrt{66}}$

Multiply $\frac{5}{2 \sqrt{66}}$ by $\frac{\sqrt{66}}{\sqrt{66}}$ .

$\frac{5}{2 \sqrt{66}} \cdot \frac{\sqrt{66}}{\sqrt{66}}$

Combine and simplify the denominator.

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Multiply $\frac{5}{2 \sqrt{66}}$ and $\frac{\sqrt{66}}{\sqrt{66}}$ .

$\frac{5 \sqrt{66}}{2 \sqrt{66} \sqrt{66}}$

Move $\sqrt{66}$ .

$\frac{5 \sqrt{66}}{2 (\sqrt{66} \sqrt{66})}$

Raise $\sqrt{66}$ to the power of $1$ .

$\frac{5 \sqrt{66}}{2 ({\sqrt{66}}^{1} \sqrt{66})}$

Raise $\sqrt{66}$ to the power of $1$ .

$\frac{5 \sqrt{66}}{2 ({\sqrt{66}}^{1} {\sqrt{66}}^{1})}$

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

$\frac{5 \sqrt{66}}{2 {\sqrt{66}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{5 \sqrt{66}}{2 {\sqrt{66}}^{2}}$

Rewrite ${\sqrt{66}}^{2}$ as $66$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{66}$ as $66^{\frac{1}{2}}$ .

$\frac{5 \sqrt{66}}{2 {(66^{\frac{1}{2}})}^{2}}$

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

$\frac{5 \sqrt{66}}{2 \cdot 66^{\frac{1}{2} \cdot 2}}$

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

$\frac{5 \sqrt{66}}{2 \cdot 66^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{5 \sqrt{66}}{2 \cdot 66^{\frac{2}{2}}}$

Divide $1$ by $1$ .

$\frac{5 \sqrt{66}}{2 \cdot 66^{1}}$

Evaluate the exponent.

$\frac{5 \sqrt{66}}{2 \cdot 66}$

Multiply $2$ by $66$ .

$\frac{5 \sqrt{66}}{132}$

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{66}}{132}$

Decimal Form:

$0.30772872 \dots$

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