# How do you simplify  sqrt(320y^2)?

Apr 30, 2016

$\sqrt{320 {y}^{2}} = 8 \sqrt{5} \left\mid y \right\mid$

#### Explanation:

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

In our example, we know that ${y}^{2} = {\left\mid y \right\mid}^{2} \ge 0$

In addition note that $320 = 64 \cdot 5 = {8}^{2} \cdot 5$

So:

$\sqrt{320 {y}^{2}} = \sqrt{{8}^{2} \cdot 5 \cdot {\left\mid y \right\mid}^{2}} = \sqrt{{8}^{2}} \cdot \sqrt{5} \cdot \sqrt{{\left\mid y \right\mid}^{2}} = 8 \sqrt{5} \left\mid y \right\mid$