# How do you simplify (5 square root 2 + square root 3)(square root 2 + 2 square root 3)?

##### 1 Answer
Jul 27, 2015

=color(blue)(16 +11sqrt(6)

#### Explanation:

Expressing the question in numbers:

$= \textcolor{b l u e}{\left(5 \sqrt{2} + \sqrt{3}\right)} \cdot \left(\sqrt{2} + 2 \sqrt{3}\right)$

Each term within the first bracket needs to be multiplied with each term within the second bracket.

$= \textcolor{b l u e}{\left(5 \sqrt{2}\right)} \cdot \left(\sqrt{2} + 2 \sqrt{3}\right) + \textcolor{b l u e}{\left(\sqrt{3}\right)} \cdot \left(\sqrt{2} + 2 \sqrt{3}\right)$

$= \left[\left(5 \sqrt{2}\right) \left(\sqrt{2}\right) + \left(5 \sqrt{2}\right) \left(2 \sqrt{3}\right)\right] + \left[\left(\sqrt{3}\right) \left(\sqrt{2}\right) + \left(\sqrt{3}\right) \cdot \left(2 \sqrt{3}\right)\right]$

$= \left[5 \cdot 2 + 10 \sqrt{2 \cdot 3}\right] + \left[\sqrt{6} + 2 \cdot 3\right]$

$= \left[10 + 10 \sqrt{6}\right] + \left[\sqrt{6} + 6\right]$

Grouping like terms

$= 16 + 11 \sqrt{6}$