# How do you add 4sqrt2+6sqrt18?

Apr 2, 2015

You always try to "take squares out of the root."

You may have noticed that $18 = 2 \cdot 9 = 2 \cdot {3}^{2}$
Now you can take the ${3}^{2}$ outside of the root and it becomes $3$.

So:

$4 \sqrt{2} + 6 \sqrt{18} = \left(4\right) \sqrt{2} + \left(3 \cdot 6\right) \sqrt{2} =$

$\left(4 + 18\right) \cdot \sqrt{2} = 22 \sqrt{2}$

(because you may add the like radicals $\sqrt{2}$)