# How do you simplify 21sqrt2+6sqrt6?

Oct 16, 2015

$3 \sqrt{2} \cdot \left(7 + 2 \sqrt{3}\right)$

#### Explanation:

There's really not much you can do to simplify this expression.

You can, however, rewrite $\sqrt{6}$ as

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

The expression becomes

$21 \sqrt{2} + 6 \cdot \sqrt{2} \cdot \sqrt{3}$

Notice that you can now use $3 \sqrt{2}$ as a common factor for the two terms to get

$3 \cdot 7 \cdot \sqrt{2} + 2 \cdot 3 \cdot \sqrt{2} \cdot \sqrt{3} = 3 \sqrt{2} \cdot \left(7 + 2 \sqrt{3}\right)$