# How do you simplify sqrt80 + sqrt125 - sqrt45 + 2 sqrt20?

May 27, 2016

$10 \sqrt{5}$

#### Explanation:

Note that each of the values under the square root sign has 5 as a factor. In addition to this, in each case the other factor is a perfect square.

$\sqrt{16 \times 5} + \sqrt{25 \times 5} - \sqrt{9 \times 5} + 2 \sqrt{4 \times 5}$

$= 4 \sqrt{5} + 5 \sqrt{5} - 3 \sqrt{5} + 2 \times 2 \sqrt{5}$

Each term is now given in terms of $\sqrt{5}$ and can be simplified to give

$10 \sqrt{5}$