# What is the square root of 8 times the square root of 20?

Jun 27, 2018

See a solution process below:

#### Explanation:

We can rewrite the expression:

$\sqrt{8} \times \sqrt{20}$

using the following rule for radicals:

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

$\sqrt{\textcolor{red}{8}} \cdot \sqrt{\textcolor{b l u e}{20}} \implies \sqrt{\textcolor{red}{8} \cdot \textcolor{b l u e}{20}} \implies \sqrt{160}$

Now, we can use this rule for radicals to simplify the radical:

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

$\sqrt{160} \implies \sqrt{\textcolor{red}{16} \cdot \textcolor{b l u e}{10}} \implies \sqrt{\textcolor{red}{16}} \cdot \sqrt{\textcolor{b l u e}{10}} \implies 4 \sqrt{10}$