# How do you add 3sqrt50 - 5sqrt18?

Apr 14, 2015

You first try to get any squares from under the root.

You may have noticed that
$50 = 2 \cdot 25 = 2 \cdot {5}^{2}$
$18 = 2 \cdot 9 = 2 \cdot {3}^{2}$

We can take these squares out the root (where they are unsquared):

$3 \sqrt{2 \cdot {5}^{2}} - 5 \sqrt{2 \cdot {3}^{2}} = 5 \cdot 3 \sqrt{2} - 3 \cdot 5 \sqrt{2}$

$= 15 \sqrt{2} - 15 \sqrt{2} = 0$