# How do you simplify 2sqrt45?

Oct 14, 2015

$2 \sqrt{45} = 6 \sqrt{5}$

#### Explanation:

The target is to write $45$ as a multiplication of some squares. Keeping the 2 aside for now.

Factorising:

$45 = 9 \times 5 = 1 \times {3}^{2} \times 5$

$\therefore 2 \sqrt{45} = 2 \sqrt{{3}^{2} \times 5} = 2 \times \left(\sqrt{{3}^{2}} \times \sqrt{5}\right) =$

$2 \times 3 \times \sqrt{5} = 6 \sqrt{5}$