Simplify square root of x/y

$\sqrt{\frac{x}{y}}$

Step 1

Rewrite $\sqrt{\frac{x}{y}}$ as $\frac{\sqrt{x}}{\sqrt{y}}$ .

$\frac{\sqrt{x}}{\sqrt{y}}$

Step 2

Multiply $\frac{\sqrt{x}}{\sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$\frac{\sqrt{x}}{\sqrt{y}} \cdot \frac{\sqrt{y}}{\sqrt{y}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{\sqrt{x}}{\sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$\frac{\sqrt{x} \sqrt{y}}{\sqrt{y} \sqrt{y}}$

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

$\frac{\sqrt{x} \sqrt{y}}{{\sqrt{y}}^{1} \sqrt{y}}$

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

$\frac{\sqrt{x} \sqrt{y}}{{\sqrt{y}}^{1} {\sqrt{y}}^{1}}$

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

$\frac{\sqrt{x} \sqrt{y}}{{\sqrt{y}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{x} \sqrt{y}}{{\sqrt{y}}^{2}}$

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

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

$\frac{\sqrt{x} \sqrt{y}}{{(y^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{x} \sqrt{y}}{y^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{x} \sqrt{y}}{y^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{x} \sqrt{y}}{y^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{x} \sqrt{y}}{y^{1}}$

Simplify.

$\frac{\sqrt{x} \sqrt{y}}{y}$

Step 4

Combine using the product rule for radicals.

$\frac{\sqrt{x y}}{y}$