# How do you simplify -sqrt45+2sqrt5-sqrt20-2sqrt6?

May 10, 2017

See a solution process below:

#### Explanation:

First, we can use this rule of radicals to simplify two of the terms:

$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$

$- \textcolor{red}{\sqrt{45}} + 2 \sqrt{5} - \textcolor{red}{\sqrt{20}} - 2 \sqrt{6} \implies$

$- \textcolor{red}{\sqrt{9 \cdot 5}} + 2 \sqrt{5} - \textcolor{red}{\sqrt{4 \cdot 5}} - 2 \sqrt{6} \implies$

$- \left(\textcolor{red}{\sqrt{9}} \cdot \textcolor{red}{\sqrt{5}}\right) + 2 \sqrt{5} - \left(\textcolor{red}{\sqrt{4}} \cdot \textcolor{red}{\sqrt{5}}\right) - 2 \sqrt{6} \implies$

$- \left(3 \textcolor{red}{\sqrt{5}}\right) + 2 \sqrt{5} - \left(2 \textcolor{red}{\sqrt{5}}\right) - 2 \sqrt{6} \implies$

$- 3 \sqrt{5} + 2 \sqrt{5} - 2 \sqrt{5} - 2 \sqrt{6}$

We can now combine like terms:

$- 3 \sqrt{5} + \left(2 - 2\right) \sqrt{5} - 2 \sqrt{6} \implies$

$- 3 \sqrt{5} + \left(0 \cdot \sqrt{5}\right) - 2 \sqrt{6} \implies$

$- 3 \sqrt{5} - 2 \sqrt{6} \implies$