Simplify square root of (5m)/(7n^2)

$\sqrt{\frac{5 m}{7 n^{2}}}$

Rewrite $\frac{5 m}{7 n^{2}}$ as ${(\frac{1}{n})}^{2} \frac{5 m}{7}$ .

Factor the perfect power $1^{2}$ out of $5 m$ .

$\sqrt{\frac{1^{2} (5 m)}{7 n^{2}}}$

Factor the perfect power $n^{2}$ out of $7 n^{2}$ .

$\sqrt{\frac{1^{2} (5 m)}{n^{2} \cdot 7}}$

Rearrange the fraction $\frac{1^{2} (5 m)}{n^{2} \cdot 7}$ .

$\sqrt{{(\frac{1}{n})}^{2} \frac{5 m}{7}}$

Pull terms out from under the radical.

$\frac{1}{n} \sqrt{\frac{5 m}{7}}$

Rewrite $\sqrt{\frac{5 m}{7}}$ as $\frac{\sqrt{5 m}}{\sqrt{7}}$ .

$\frac{1}{n} \cdot \frac{\sqrt{5 m}}{\sqrt{7}}$

Multiply $\frac{\sqrt{5 m}}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{1}{n} (\frac{\sqrt{5 m}}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}})$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{5 m}}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{1}{n} \cdot \frac{\sqrt{5 m} \sqrt{7}}{\sqrt{7} \sqrt{7}}$

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{1}{n} \cdot \frac{\sqrt{5 m} \sqrt{7}}{{\sqrt{7}}^{1} \sqrt{7}}$

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{1}{n} \cdot \frac{\sqrt{5 m} \sqrt{7}}{{\sqrt{7}}^{1} {\sqrt{7}}^{1}}$

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

$\frac{1}{n} \cdot \frac{\sqrt{5 m} \sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{1}{n} \cdot \frac{\sqrt{5 m} \sqrt{7}}{{\sqrt{7}}^{2}}$

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\frac{1}{n} \cdot \frac{\sqrt{5 m} \sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}$

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

$\frac{1}{n} \cdot \frac{\sqrt{5 m} \sqrt{7}}{7^{\frac{1}{2} \cdot 2}}$

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

$\frac{1}{n} \cdot \frac{\sqrt{5 m} \sqrt{7}}{7^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{1}{n} \cdot \frac{\sqrt{5 m} \sqrt{7}}{7^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{1}{n} \cdot \frac{\sqrt{5 m} \sqrt{7}}{7^{1}}$

Evaluate the exponent.

$\frac{1}{n} \cdot \frac{\sqrt{5 m} \sqrt{7}}{7}$

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{1}{n} \cdot \frac{\sqrt{5 m \cdot 7}}{7}$

Multiply $7$ by $5$ .

$\frac{1}{n} \cdot \frac{\sqrt{35 m}}{7}$

Combine fractions.

Multiply $\frac{1}{n}$ by $\frac{\sqrt{35 m}}{7}$ .

$\frac{\sqrt{35 m}}{n \cdot 7}$

Move $7$ to the left of $n$ .

$\frac{\sqrt{35 m}}{7 n}$

Simplify square root of (5m)/(7n^2)

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