Simplify 8 square root of 5/32

$8 \sqrt{\frac{5}{32}}$

Rewrite $\sqrt{\frac{5}{32}}$ as $\frac{\sqrt{5}}{\sqrt{32}}$ .

$8 \frac{\sqrt{5}}{\sqrt{32}}$

Simplify the denominator.

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Rewrite $32$ as $4^{2} \cdot 2$ .

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Factor $16$ out of $32$ .

$8 \frac{\sqrt{5}}{\sqrt{16 (2)}}$

Rewrite $16$ as $4^{2}$ .

$8 \frac{\sqrt{5}}{\sqrt{4^{2} \cdot 2}}$

Pull terms out from under the radical.

$8 \frac{\sqrt{5}}{4 \sqrt{2}}$

Simplify terms.

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Cancel the common factor of $4$ .

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Factor $4$ out of $8$ .

$4 (2) \frac{\sqrt{5}}{4 \sqrt{2}}$

Factor $4$ out of $4 \sqrt{2}$ .

$4 (2) \frac{\sqrt{5}}{4 (\sqrt{2})}$

Cancel the common factor.

$4 \cdot 2 \frac{\sqrt{5}}{4 \sqrt{2}}$

Rewrite the expression.

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

Combine $2$ and $\frac{\sqrt{5}}{\sqrt{2}}$ .

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

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

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

Combine and simplify the denominator.

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

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

Raise $\sqrt{2}$ to the power of $1$ .

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

Raise $\sqrt{2}$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Divide $1$ by $1$ .

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

Evaluate the exponent.

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Divide $\sqrt{5} \sqrt{2}$ by $1$ .

$\sqrt{5} \sqrt{2}$

Combine using the product rule for radicals.

$\sqrt{5 \cdot 2}$

Multiply $5$ by $2$ .

$\sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{10}$

Decimal Form:

$3.16227766 \dots$

Simplify 8 square root of 5/32