# How do you simplify sqrt 20 - sqrt 5 + sqrt 45?

Feb 21, 2016

$4 \sqrt{5}$

#### Explanation:

Attempt to rewrite all the radicals in terms of $\sqrt{5}$

consider the factors of 20 - ± ( 1,2,4,5,10,20 )
We want 4 and 5.

since $\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2 \sqrt{5}$

[ making use of $\sqrt{a} \times \sqrt{b} = \sqrt{a} b \Leftrightarrow \sqrt{a} b = \sqrt{a} \times \sqrt{b}$]

now consider the factors of 45 - ± (1,3,5,9,15,45 )
We want 9 and 5.

since $\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3 \sqrt{5}$

$\Rightarrow \sqrt{20} - \sqrt{5} + \sqrt{45} = 2 \sqrt{5} - \sqrt{5} + 3 \sqrt{5} = 4 \sqrt{5}$