# How do you simplify 3sqrt20 + 2sqrt45?

May 1, 2016

$12 \sqrt{5}$

#### Explanation:

In most questions involving powers and roots, a good strategy is to break numbers down into their prime factors. This tells us what we are working with.

$3 \sqrt{4 \times 5} + 2 \sqrt{9 \times 5}$

4 and 9 are square numbers, they have exact square roots.

= $3 \times 2 \sqrt{5} + 2 \times 3 \sqrt{5}$

= $6 \sqrt{5} + 6 \sqrt{5}$

= $12 \sqrt{5}$