How do you simplify 6sqrt6 + 6sqrt3?

Oct 9, 2015

$6 \sqrt{3} \cdot \left(\sqrt{2} + 1\right)$

Explanation:

You can start by writing

$\sqrt{6} = \sqrt{2 \cdot 3} = \sqrt{2} \cdot \sqrt{3}$

The expression will thus be

$6 \cdot \sqrt{2} \cdot \sqrt{3} + 6 \sqrt{3} = \sqrt{2} \cdot 6 \sqrt{3} + 6 \sqrt{3}$

Now use $6 \sqrt{3}$ as a common factor to get the simplified form

$\sqrt{2} \cdot 6 \sqrt{3} + 6 \sqrt{3} = \textcolor{g r e e n}{6 \sqrt{3} \cdot \left(\sqrt{2} + 1\right)}$