# How do you simplify 6sqrt343 - 2 sqrt7?

Mar 16, 2018

See a solution process below:

#### Explanation:

First, rewrite the radical on the left as:

$6 \sqrt{49 \cdot 7} - 2 \sqrt{7}$

Next, use this rule for radicals to simplify the term on the left:

$\sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}}$

$6 \sqrt{\textcolor{red}{49} \cdot \textcolor{b l u e}{7}} - 2 \sqrt{7} \implies$

$6 \sqrt{\textcolor{red}{49}} \sqrt{\textcolor{b l u e}{7}} - 2 \sqrt{7} \implies$

$\left(6 \cdot 7 \sqrt{\textcolor{b l u e}{7}}\right) - 2 \sqrt{7} \implies$

$42 \sqrt{\textcolor{b l u e}{7}} - 2 \sqrt{7}$

Now, factor out the common term to complete the simplification:

$\left(42 - 2\right) \sqrt{7} \implies$

$40 \sqrt{7}$