# How do you simplify 2 sqrt 8 - 2 sqrt 2?

Mar 3, 2018

$2 \sqrt{8} - 2 \sqrt{2}$

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

$= 4 \sqrt{2} - 2 \sqrt{2}$

$= 2 \sqrt{2}$

Mar 3, 2018

See a solution process below:

#### Explanation:

First rewrite the radical on the left using this rule for radicals:

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

$2 \sqrt{8} - 2 \sqrt{2} \implies$

$2 \sqrt{\textcolor{red}{4} \cdot \textcolor{b l u e}{2}} - 2 \sqrt{2} \implies$

$2 \sqrt{\textcolor{red}{4}} \sqrt{\textcolor{b l u e}{2}} - 2 \sqrt{2} \implies$

$\left(2 \cdot 2\right) \sqrt{\textcolor{b l u e}{2}} - 2 \sqrt{2} \implies$

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

Now, we can factor out the common term to complete the simplification:

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

$2 \sqrt{2}$