# How do you simplify 2 sqrt 3 - 4 sqrt 2 + 6 sqrt3 + 8 sqrt 2?

Combine like terms and factor to get to $4 \sqrt{2} \left(\sqrt{6} + 1\right)$

#### Explanation:

We can combine like terms, so the terms with $\sqrt{3}$ in them can be combined and those with $\sqrt{2}$ can be combined, like this:

$2 \sqrt{3} - 4 \sqrt{2} + 6 \sqrt{3} + 8 \sqrt{2}$

$2 \sqrt{3} + 6 \sqrt{3} + 8 \sqrt{2} - 4 \sqrt{2}$

$8 \sqrt{3} + 4 \sqrt{2}$

We can then factor out a 4 from each term, to get:

$4 \left(2 \sqrt{3} + \sqrt{2}\right)$

We can also write $2 \sqrt{3}$ as:

$4 \left(\sqrt{2} \sqrt{2} \sqrt{3} + \sqrt{2}\right)$

so we can factor out another $\sqrt{2}$:

$4 \sqrt{2} \left(\sqrt{6} + 1\right)$