# How do you simplify: Square root of 50 + square root of 18?

Jul 12, 2015

$8 \sqrt{2}$

#### Explanation:

Recall the multiplicative property of square root for positive $a$ and $b$:
$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$

Using this rule, we can write
$\sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5 \sqrt{2}$

analogously,
$\sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3 \sqrt{2}$

Adding them together and using the distributive law, we have
$\sqrt{50} + \sqrt{18} = 5 \sqrt{2} + 3 \sqrt{2} = 8 \sqrt{2}$