Simplify square root of 10/(13r^3)

$\sqrt{\frac{10}{13 r^{3}}}$

Rewrite $\frac{10}{13 r^{3}}$ as ${(\frac{1}{r})}^{2} \frac{10}{13 r}$ .

Factor the perfect power $1^{2}$ out of $10$ .

$\sqrt{\frac{1^{2} \cdot 10}{13 r^{3}}}$

Factor the perfect power $r^{2}$ out of $13 r^{3}$ .

$\sqrt{\frac{1^{2} \cdot 10}{r^{2} \cdot (13 r)}}$

Rearrange the fraction $\frac{1^{2} \cdot 10}{r^{2} \cdot (13 r)}$ .

$\sqrt{{(\frac{1}{r})}^{2} \frac{10}{13 r}}$

Pull terms out from under the radical.

$\frac{1}{r} \sqrt{\frac{10}{13 r}}$

Rewrite $\sqrt{\frac{10}{13 r}}$ as $\frac{\sqrt{10}}{\sqrt{13 r}}$ .

$\frac{1}{r} \cdot \frac{\sqrt{10}}{\sqrt{13 r}}$

Multiply $\frac{\sqrt{10}}{\sqrt{13 r}}$ by $\frac{\sqrt{13 r}}{\sqrt{13 r}}$ .

$\frac{1}{r} (\frac{\sqrt{10}}{\sqrt{13 r}} \cdot \frac{\sqrt{13 r}}{\sqrt{13 r}})$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{10}}{\sqrt{13 r}}$ by $\frac{\sqrt{13 r}}{\sqrt{13 r}}$ .

$\frac{1}{r} \cdot \frac{\sqrt{10} \sqrt{13 r}}{\sqrt{13 r} \sqrt{13 r}}$

Raise $\sqrt{13 r}$ to the power of $1$ .

$\frac{1}{r} \cdot \frac{\sqrt{10} \sqrt{13 r}}{{\sqrt{13 r}}^{1} \sqrt{13 r}}$

Raise $\sqrt{13 r}$ to the power of $1$ .

$\frac{1}{r} \cdot \frac{\sqrt{10} \sqrt{13 r}}{{\sqrt{13 r}}^{1} {\sqrt{13 r}}^{1}}$

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

$\frac{1}{r} \cdot \frac{\sqrt{10} \sqrt{13 r}}{{\sqrt{13 r}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{1}{r} \cdot \frac{\sqrt{10} \sqrt{13 r}}{{\sqrt{13 r}}^{2}}$

Rewrite ${\sqrt{13 r}}^{2}$ as $13 r$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{13 r}$ as ${(13 r)}^{\frac{1}{2}}$ .

$\frac{1}{r} \cdot \frac{\sqrt{10} \sqrt{13 r}}{{({(13 r)}^{\frac{1}{2}})}^{2}}$

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

$\frac{1}{r} \cdot \frac{\sqrt{10} \sqrt{13 r}}{{(13 r)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{1}{r} \cdot \frac{\sqrt{10} \sqrt{13 r}}{{(13 r)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{1}{r} \cdot \frac{\sqrt{10} \sqrt{13 r}}{{(13 r)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{1}{r} \cdot \frac{\sqrt{10} \sqrt{13 r}}{{(13 r)}^{1}}$

Simplify.

$\frac{1}{r} \cdot \frac{\sqrt{10} \sqrt{13 r}}{13 r}$

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{1}{r} \cdot \frac{\sqrt{10 (13 r)}}{13 r}$

Multiply $10$ by $13$ .

$\frac{1}{r} \cdot \frac{\sqrt{130 r}}{13 r}$

Multiply $\frac{1}{r} \cdot \frac{\sqrt{130 r}}{13 r}$ .

Multiply $\frac{1}{r}$ by $\frac{\sqrt{130 r}}{13 r}$ .

$\frac{\sqrt{130 r}}{r (13 r)}$

Raise $r$ to the power of $1$ .

$\frac{\sqrt{130 r}}{13 (r^{1} r)}$

Raise $r$ to the power of $1$ .

$\frac{\sqrt{130 r}}{13 (r^{1} r^{1})}$

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

$\frac{\sqrt{130 r}}{13 r^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{130 r}}{13 r^{2}}$

Simplify square root of 10/(13r^3)

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