# How do you simplify sqrt2(sqrt6+sqrt8)+sqrt3?

##### 1 Answer
Jun 7, 2015

We are going to expand :

$= \sqrt{2} \cdot \sqrt{6} + \sqrt{2} \cdot \sqrt{8} + \sqrt{3}$
$= \sqrt{12} + \sqrt{16} + \sqrt{3}$
$= \sqrt{4 \cdot 3} + 4 + \sqrt{3}$ ( since $\sqrt{16} = 4$ )
$= \sqrt{4} \cdot \sqrt{3} + 4 + \sqrt{3}$
$= 2 \sqrt{3} + 4 + \sqrt{3}$ ( since $\sqrt{4} = 2$ )
$= 3 \sqrt{3} + 4$