# How do you simplify sqrt(320)?

Apr 18, 2018

$8 \sqrt{5}$

#### Explanation:

split the number into a product pair with one being a perfect square. If you can not find the largest perfect square to begin with, start with a smaller one

$\sqrt{320} = \sqrt{16 \times 20}$

$= \sqrt{16} \times \sqrt{20} = 2 \sqrt{20}$

we continue this process until there are no more perfect squares

$4 \sqrt{20} = 4 \sqrt{4 \times 5}$

$= 4 \sqrt{4} \sqrt{5}$

$= 4 \times 2 \sqrt{5}$

$= 8 \sqrt{5}$