# How do you multiply sqrt2(3sqrt14 - sqrt7)?

Mar 27, 2018

$6 \sqrt{7} - \sqrt{14}$

#### Explanation:

Multiply $\sqrt{2}$ by each term in the parentheses

$\sqrt{2} \left(3 \sqrt{14} - \sqrt{7}\right)$

$\sqrt{2} \cdot 3 \sqrt{14} - \sqrt{2} \cdot \sqrt{7}$

$3 \sqrt{28} - \sqrt{14} \rightarrow 3 \sqrt{28}$ can be simplified

$3 \sqrt{28} = 3 \sqrt{4} \cdot \sqrt{7} \rightarrow$ $4$ is a perfect square

$6 \cdot \sqrt{7} = 6 \sqrt{7} = 3 \sqrt{28}$

$6 \sqrt{7} - \sqrt{14}$