# How do you simplify (2 sqrt(7) + sqrt(3)) times (3 sqrt(7) - sqrt(2))?

Sep 4, 2016

The value is $42 - 2 \sqrt{14} + 3 \sqrt{21} - \sqrt{6}$

#### Explanation:

$\left(2 \sqrt{7} + \sqrt{3}\right) \times \left(3 \sqrt{7} - \sqrt{2}\right)$
$= 6 \cdot 7 - 2 \sqrt{7} \sqrt{2} + 3 \sqrt{7} \sqrt{3} - \sqrt{2} \sqrt{3}$
$= 42 - 2 \sqrt{14} + 3 \sqrt{21} - \sqrt{6}$

In these calculations I used the following properties of square roots:

1. $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$

2. $\sqrt{a \cdot a} = a$