# How do you simplify 4√5 - 2√45?

Oct 9, 2015

$- 2 \sqrt{5}$

#### Explanation:

Your starting expression looks like this

$4 \sqrt{5} - 2 \sqrt{45}$

Notice that you can write $45$ as

$45 = 3 \cdot 15 = 3 \cdot 3 \cdot 5 = {3}^{2} \cdot 5$

This means that you have

$4 \sqrt{5} - 2 \sqrt{{3}^{2} \cdot 5} = 4 \sqrt{5} - 2 \cdot \sqrt{{3}^{2}} \cdot \sqrt{5}$

$= 4 \sqrt{5} - 2 \cdot 3 \sqrt{5}$

$= 4 \sqrt{5} - 6 \sqrt{5}$

$= \sqrt{5} \cdot \left(4 - 6\right)$

$= \textcolor{g r e e n}{- 2 \sqrt{5}}$