Simplify square root of (xy)/z

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

Step 1

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

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

Step 2

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

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

Step 3

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 4

Combine using the product rule for radicals.

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