# How do you simplify square root of 4y^3 - square root y^3?

Sep 16, 2015

$\sqrt{4 {y}^{3}} - \sqrt{{y}^{3}} = y \sqrt{y}$

#### Explanation:

The useful rule for square roots here is that $\sqrt{a b} = \sqrt{a} \sqrt{b}$

This means that $\sqrt{4 {y}^{3}} = \sqrt{4 {y}^{2} y} = \sqrt{4} \sqrt{{y}^{2}} \sqrt{y}$, which can be simplified to $2 y \sqrt{y}$

$\sqrt{{y}^{3}}$ is similarly simplified to $\sqrt{{y}^{2} y} = \sqrt{{y}^{2}} \sqrt{y} = y \sqrt{y}$.

Subtracting the second from the first gives us
$2 y \sqrt{y} - y \sqrt{y} = y \sqrt{y}$