# How do you simplify: the square root of 6 (7 the square root of 3 + 6)?

Aug 3, 2015

=color(blue)(21sqrt2 + 6sqrt6

#### Explanation:

Square root of 6 (7 the square root of 3 + 6).

Expressing the question in numbers:

$= \textcolor{b l u e}{\sqrt{6} \cdot} \left(7 \sqrt{3} + 6\right)$

$= \textcolor{b l u e}{\sqrt{6}} \cdot \left(7 \sqrt{3}\right) + \textcolor{b l u e}{\left(\sqrt{6}\right)} \left(6\right)$

$= 7 \sqrt{3.} \sqrt{6} + \sqrt{6} \cdot \left(6\right)$

$= 7 \sqrt{3 \cdot 6} + 6 \sqrt{6}$

$= 7 \sqrt{3 \cdot 3 \cdot 2} + 6 \sqrt{6}$

$= 7 \cdot 3 \sqrt{2} + 6 \sqrt{6}$

=color(blue)(21sqrt2 + 6sqrt6