# How do you simplify 2 sqrt 20 + 45 sqrt20?

Mar 4, 2016

• Factorize inside the square roots
• Use some simple root rules
• Voilá!

#### Explanation:

So we have $2 \sqrt{20} + 45 \sqrt{20}$

Let's factorize a bit..

$2 \sqrt{2 \cdot 2 \cdot 5} + 45 \sqrt{2 \cdot 2 \cdot 5}$

$= 2 \sqrt{4 \cdot 5} + 45 \sqrt{4 \cdot 5}$

$= 2 \sqrt{4} \cdot \sqrt{5} + 45 \sqrt{4} \cdot \sqrt{5}$

$= 2 \cdot 2 \sqrt{5} + 45 \cdot 2 \sqrt{5}$

$= 4 \sqrt{5} + 90 \sqrt{5}$

$= 94 \sqrt{5}$