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

Nov 23, 2017

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

#### Explanation:

$2 \sqrt{20} - \sqrt{20} + 3 \sqrt{20} - 2 \sqrt{45}$

= $\sqrt{20} \left(2 - 1 + 3\right) - 2 \sqrt{3 \times 3 \times 5}$

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

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

= $8 \sqrt{5} - 6 \sqrt{5}$

= $\left(8 - 6\right) \sqrt{5}$

= $2 \sqrt{5}$

Nov 23, 2017

$2 \sqrt{5}$

#### Explanation:

Simplify
$2 \sqrt{20} - \sqrt{20} + 3 \sqrt{20} - 2 \sqrt{45}$

1) Combine like terms
Combine all the coefficients of the $\sqrt{20}$ terms
$4 \sqrt{20} - 2 \sqrt{45}$

2) Factor to get perfect squares
$4 \sqrt{{2}^{2} \cdot 5} - 2 \sqrt{{3}^{2} \cdot 5}$

3) Find the square roots, but leave the 5s inside
$\left(2 \cdot 4\right) \sqrt{5} - \left(3 \cdot 2\right) \sqrt{5}$

This is the same as
$8 \sqrt{5} - 6 \sqrt{5}$

4) Combine like terms
$2 \sqrt{5} \leftarrow$ answer

Simplified, the expression is $2 \sqrt{5}$