# What is the answer to the square root of 50 + square root of 8 - square root of 18?

Jul 30, 2015

=color(green)(4sqrt2

#### Explanation:

Prime factorising each of the numbers in order to simplify the terms:

$\sqrt{50} = \sqrt{5 \cdot 5 \cdot 2} = 5 \sqrt{2}$

$\sqrt{8} = \sqrt{2 \cdot 2 \cdot 2} = 2 \sqrt{2}$

$\sqrt{18} = \sqrt{2 \cdot 3 \cdot 3} = 3 \sqrt{2}$

Now,

$\sqrt{50} + \sqrt{8} - \sqrt{18} = 5 \sqrt{2} + 2 \sqrt{2} - 3 \sqrt{2}$

=color(green)(4sqrt2