# How do you simplify 3sqrt18+3sqrt12+2sqrt27?

Aug 22, 2016

$9 \sqrt{2} + 12 \sqrt{3}$

#### Explanation:

Write each number as the product of its prime factors first.
Look for squares of factors.

$3 \sqrt{18} = 3 \times \sqrt{2 \times 3 \times 3} = 3 \times 3 \sqrt{2}$

$3 \sqrt{12} = 3 \times \sqrt{2 \times 2 \times 3} = 3 \times 2 \sqrt{3}$

$2 \sqrt{27} = 2 \times \sqrt{3 \times 3 \times 3} = 2 \times 3 \sqrt{3}$

$3 \sqrt{18} + 3 \sqrt{12} + 2 \sqrt{27}$

=$9 \sqrt{2} + \textcolor{red}{6 \sqrt{3} + 6 \sqrt{3}}$

=$9 \sqrt{2} + \textcolor{red}{12 \sqrt{3}}$