# How do you simplify sqrt(150x^2y)?

Jan 19, 2016

$\sqrt{150 {x}^{2} y} = 5 \left\mid x \right\mid \sqrt{6 y}$

#### Explanation:

If $a , b \ge 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$

Note also that $\sqrt{{x}^{2}} = \left\mid x \right\mid$ for any Real number $x$

So:

$\sqrt{150 {x}^{2} y} = \sqrt{25 \cdot 6 \cdot {x}^{2} \cdot y} = \sqrt{{5}^{2}} \cdot \sqrt{6 {x}^{2} y} = 5 \sqrt{6 {x}^{2} y}$

$= 5 \sqrt{{x}^{2}} \sqrt{6 y} = 5 \left\mid x \right\mid \sqrt{6 y}$