# How do you simplify sqrt(x^3y^5)?

Jul 7, 2015

Simplify the square root according to the explanation.

#### Explanation:

$\sqrt{{x}^{3} {y}^{5}}$ =

Simplify.

$\sqrt{{x}^{2}} \sqrt{x} \sqrt{{y}^{4}} \sqrt{y}$ =

Simplify $\sqrt{{x}^{2}}$ to $x$.

$x \sqrt{x} \sqrt{{y}^{4}} \sqrt{y}$ =

Simplify $\sqrt{{y}^{4}}$ to $\sqrt{{y}^{2}}$.

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

Simplify.

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

Jul 7, 2015

$\sqrt{{x}^{3} {y}^{5}} = \left\mid x \right\mid {y}^{2} \sqrt{x y}$

#### Explanation:

$\sqrt{{x}^{3} {y}^{5}}$
$\textcolor{w h i t e}{\text{XXXX}}$$= \sqrt{{x}^{3}} \cdot \sqrt{{y}^{5}}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \sqrt{{x}^{2} \cdot x} \cdot \sqrt{{\left({y}^{2}\right)}^{2} \cdot y}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \sqrt{{x}^{2}} \cdot \sqrt{x} \cdot \sqrt{{\left({y}^{2}\right)}^{2}} \cdot \sqrt{y}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \left\mid x \right\mid \sqrt{x} \cdot {y}^{2} \sqrt{y}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \left\mid x \right\mid {y}^{2} \sqrt{x y}$