# How do you simplify -sqrt6(2sqrt6-4sqrt2)?

Jun 14, 2018

$- 12 + 8 \sqrt{3}$

#### Explanation:

We can distribute the $- \sqrt{6}$ to both terms on the parenthesis. Doing this, we get

$- 2 \sqrt{6 \cdot 6} + 4 \sqrt{2 \cdot 6}$

This simplifies to

$- 2 \sqrt{36} + \textcolor{b l u e}{4 \sqrt{12}}$

Which can be rewritten as

$- 12 + \textcolor{b l u e}{4 \cdot \sqrt{4 \cdot 3}}$

$\implies - 12 + \textcolor{b l u e}{4 \cdot 2 \sqrt{3}}$

Which finally simplifies to

$- 12 + 8 \sqrt{3}$

Hope this helps!

Jun 14, 2018

expand the bracket

$- 2 \sqrt{36} + 4 \sqrt{12}$

$\sqrt{36} = 6$ and $\sqrt{12} = 2 \sqrt{3}$

$- 12 + 8 \sqrt{3}$