# How do you simplify -4sqrt8*sqrt10?

Jul 3, 2017

See a solution process below:

#### Explanation:

First, use this rule for radicals to rewrite the expression:

$\sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}}$

$- 4 \sqrt{\textcolor{red}{8}} \cdot \sqrt{\textcolor{b l u e}{10}} = - 4 \sqrt{\textcolor{red}{8} \cdot \textcolor{b l u e}{10}} = - 4 \sqrt{80}$

Next, rewrite the expression and use the same rule for radicals:

$- 4 \sqrt{80} = - 4 \sqrt{\textcolor{red}{16} \cdot \textcolor{b l u e}{5}} = - 4 \sqrt{\textcolor{red}{16}} \cdot \sqrt{\textcolor{b l u e}{5}} = \left(- 4 \cdot 4\right) \sqrt{5} =$

$- 16 \sqrt{5}$