# How do you simplify 4 square root of 27 - square root of 75?

Jul 19, 2015

First get some squares out from under the root

#### Explanation:

$27 = {3}^{2} \cdot 3 \to \sqrt{27} = \sqrt{{3}^{2}} \cdot \sqrt{3} = 3 \sqrt{3}$

$75 = {5}^{2} \cdot 3 \to \sqrt{75} = \sqrt{{5}^{2}} \cdot \sqrt{3} = 5 \sqrt{3}$

$4 \sqrt{27} - \sqrt{75} = 4 \cdot 3 \sqrt{3} - 5 \sqrt{3} = 7 \sqrt{3}$