# How do you simplify sqrt5(sqrt2+4sqrt2)?

Aug 22, 2017

See a solution process below:

#### Explanation:

First, we can factor a $\sqrt{2}$ out of each term in the parenthesis:

$\sqrt{5} \left(\sqrt{2} + 4 \sqrt{2}\right) \implies$

$\sqrt{5} \sqrt{2} \left(1 + 4\right) \implies$

$\sqrt{5} \sqrt{2} \left(5\right) \implies$

$5 \sqrt{5} \sqrt{2}$

We can now use this rule for radicals to simplify the radicals:

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

$5 \sqrt{5 \cdot 2}$

$5 \sqrt{10}$