# How do you simplify 5 square root 6 minus 4 square root 10 minus square root 6 plus 12 square root 10?

Sep 9, 2015

$4 \cdot \left(\sqrt{6} + 2 \sqrt{10}\right)$

#### Explanation:

Your starting expression (probably) looks like this

$5 \sqrt{6} - 4 \sqrt{10} - \sqrt{6} + 12 \sqrt{10}$

You can regroup the like-terms to get

$5 \sqrt{6} - \sqrt{6} - 4 \sqrt{10} + 12 \sqrt{10}$

Now you can factorize like-terms to get

$\sqrt{6} \cdot \left(5 - 1\right) + \sqrt{10} \cdot \left(12 - 4\right)$

$4 \sqrt{6} + 8 \sqrt{10}$

All you can do now is factor this expression

$4 \sqrt{6} + 4 \cdot 2 \cdot \sqrt{10} = \textcolor{g r e e n}{4 \cdot \left(\sqrt{6} + 2 \sqrt{10}\right)}$