# How do you simplify -sqrt27-3sqrt45-sqrt20+2sqrt45?

Apr 25, 2017

$- 3 \sqrt{3} - 5 \sqrt{5}$

#### Explanation:

Given:$\text{ } - \sqrt{27} - 3 \sqrt{45} - \sqrt{20} + 2 \sqrt{45}$

First note that amongst this we have:

$\text{ } - 3 \sqrt{45} + 2 \sqrt{45} \to - \sqrt{45}$

So the initial expression becomes$\text{ } - \sqrt{27} - \sqrt{45} - \sqrt{20}$

Now we are looking for squared value we can take 'outside' the roots.

Write as:$\text{ } - \sqrt{3 \times {3}^{2}} - \sqrt{5 \times {3}^{2}} - \sqrt{5 \times {2}^{2}}$

$- 3 \sqrt{3} - 3 \sqrt{5} - 2 \sqrt{5}$

$- 3 \sqrt{3} - 5 \sqrt{5}$