Simplify square root of (3a^2)/(10b^6)

$\sqrt{\frac{3 a^{2}}{10 b^{6}}}$

Rewrite $\frac{3 a^{2}}{10 b^{6}}$ as ${(\frac{a}{b^{3}})}^{2} \frac{3}{10}$ .

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

$\sqrt{\frac{a^{2} \cdot 3}{10 b^{6}}}$

Factor the perfect power ${(b^{3})}^{2}$ out of $10 b^{6}$ .

$\sqrt{\frac{a^{2} \cdot 3}{{(b^{3})}^{2} \cdot 10}}$

Rearrange the fraction $\frac{a^{2} \cdot 3}{{(b^{3})}^{2} \cdot 10}$ .

$\sqrt{{(\frac{a}{b^{3}})}^{2} \frac{3}{10}}$

Pull terms out from under the radical.

$\frac{a}{b^{3}} \sqrt{\frac{3}{10}}$

Rewrite $\sqrt{\frac{3}{10}}$ as $\frac{\sqrt{3}}{\sqrt{10}}$ .

$\frac{a}{b^{3}} \cdot \frac{\sqrt{3}}{\sqrt{10}}$

Combine.

$\frac{a \sqrt{3}}{b^{3} \sqrt{10}}$

Multiply $\frac{a \sqrt{3}}{b^{3} \sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{a \sqrt{3}}{b^{3} \sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

Combine and simplify the denominator.

Multiply $\frac{a \sqrt{3}}{b^{3} \sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{a \sqrt{3} \sqrt{10}}{b^{3} \sqrt{10} \sqrt{10}}$

Move $\sqrt{10}$ .

$\frac{a \sqrt{3} \sqrt{10}}{b^{3} (\sqrt{10} \sqrt{10})}$

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{a \sqrt{3} \sqrt{10}}{b^{3} ({\sqrt{10}}^{1} \sqrt{10})}$

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{a \sqrt{3} \sqrt{10}}{b^{3} ({\sqrt{10}}^{1} {\sqrt{10}}^{1})}$

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

$\frac{a \sqrt{3} \sqrt{10}}{b^{3} {\sqrt{10}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{a \sqrt{3} \sqrt{10}}{b^{3} {\sqrt{10}}^{2}}$

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$\frac{a \sqrt{3} \sqrt{10}}{b^{3} {(10^{\frac{1}{2}})}^{2}}$

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

$\frac{a \sqrt{3} \sqrt{10}}{b^{3} \cdot 10^{\frac{1}{2} \cdot 2}}$

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

$\frac{a \sqrt{3} \sqrt{10}}{b^{3} \cdot 10^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{a \sqrt{3} \sqrt{10}}{b^{3} \cdot 10^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{a \sqrt{3} \sqrt{10}}{b^{3} \cdot 10^{1}}$

Evaluate the exponent.

$\frac{a \sqrt{3} \sqrt{10}}{b^{3} \cdot 10}$

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{a \sqrt{10 \cdot 3}}{b^{3} \cdot 10}$

Multiply $10$ by $3$ .

$\frac{a \sqrt{30}}{b^{3} \cdot 10}$

Move $10$ to the left of $b^{3}$ .

$\frac{a \sqrt{30}}{10 b^{3}}$

Simplify square root of (3a^2)/(10b^6)

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