# How do you simplify 5 sqrt 2 - 8 sqrt 2+ 2sqrt 18?

May 9, 2018

$3 \sqrt{2}$

#### Explanation:

We can start by rewriting $\sqrt{18}$ as $\sqrt{9 \cdot 2}$ which simplifies to $3 \sqrt{2}$. Thus, our new expression is

$5 \sqrt{2} - 8 \sqrt{2} + 2 \left(3\right) \sqrt{2}$

$\implies 5 \sqrt{2} - 8 \sqrt{2} + 6 \sqrt{2}$

All of the terms have a $\sqrt{2}$ in common, so I can factor that out to get

$\sqrt{2} \left(5 - 8 + 6\right)$

$\implies 3 \sqrt{2}$

Hope this helps!