# How do you simplify 5 sqrt 72 + sqrt 75- sqrt 288?

Jan 5, 2016

$= 18 \sqrt{2} + 5 \sqrt{3}$

#### Explanation:

Break each number down into its factors
5sqrt(72) + sqrt(75) - sqrt(288))
$= 5 \sqrt{6 \cdot 6 \cdot 2} + \sqrt{5 \cdot 5 \cdot 3} - \sqrt{12 \cdot 12 \cdot 2}$
You can then take out the numbers which are duplicated, as for example $\sqrt{12 \cdot 12}$ is $12$
$= 5 \cdot 6 \sqrt{2} + 5 \sqrt{3} - 12 \sqrt{2}$
$= 30 \sqrt{2} - 12 \sqrt{2} + 5 \sqrt{3}$
$= 18 \sqrt{2} + 5 \sqrt{3}$