# How do you simplify sqrt5(10-4sqrt2)?

Jun 19, 2016

 = color(green)(10sqrt5 - 4 sqrt 10

#### Explanation:

$\sqrt{5} \left(10 - 4 \sqrt{2}\right)$

$= \textcolor{b l u e}{\sqrt{5}} \cdot \left(10 - 4 \sqrt{2}\right)$

We multiply color(blue)(sqrt5 with each of the two terms within brackets.

$= \textcolor{b l u e}{\sqrt{5}} \cdot \left(10\right) + \textcolor{b l u e}{\sqrt{5}} \cdot \left(- 4 \sqrt{2}\right)$

$= 10 \sqrt{5} + \left(- 4\right) \cdot \sqrt{2} \cdot \sqrt{5}$

$= 10 \sqrt{5} - 4 \cdot \sqrt{2 \cdot 5}$

$= 10 \sqrt{5} - 4 \sqrt{10}$