Simplify the Radical Expression square root of m/n

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

Step 1

Rewrite $\sqrt{\frac{m}{n}}$ as $\frac{\sqrt{m}}{\sqrt{n}}$ .

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

Step 2

Multiply $\frac{\sqrt{m}}{\sqrt{n}}$ by $\frac{\sqrt{n}}{\sqrt{n}}$ .

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

Step 3

Combine and simplify the denominator.

Multiply $\frac{\sqrt{m}}{\sqrt{n}}$ by $\frac{\sqrt{n}}{\sqrt{n}}$ .

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

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

$\frac{\sqrt{m} \sqrt{n}}{{\sqrt{n}}^{1} \sqrt{n}}$

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

$\frac{\sqrt{m} \sqrt{n}}{{\sqrt{n}}^{1} {\sqrt{n}}^{1}}$

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

$\frac{\sqrt{m} \sqrt{n}}{{\sqrt{n}}^{1 + 1}}$

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{\sqrt{m} \sqrt{n}}{n^{1}}$

Simplify.

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

Step 4

Combine using the product rule for radicals.

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