# What is square root of 8 plus square root of 18 minus the square root of 32?

Jul 20, 2015

$9 \sqrt{2}$

#### Explanation:

The main property this problem is based upon is the property of a square root of a product of two positive numbers:
$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$
(for any positive $a$ and $b$).
This property is easy to prove directly from the definition of a square root of a positive number.

Using this for the numbers in this problem, we get:

$\sqrt{8} + \sqrt{18} + \sqrt{32} = \sqrt{4 \cdot 2} + \sqrt{9 \cdot 2} + \sqrt{16 \cdot 2} =$
$= \sqrt{4} \cdot \sqrt{2} + \sqrt{9} \cdot \sqrt{2} + \sqrt{16} \cdot \sqrt{2} =$
$2 \sqrt{2} + 3 \sqrt{2} + 4 \sqrt{2} = 9 \sqrt{2}$