# How do you simplify 5sqrt2 + 3sqrt50 - sqrt75?

Sep 20, 2015

$20 \sqrt{2} - 5 \sqrt{3}$

#### Explanation:

$5 \sqrt{2} + 3 \sqrt{2 \cdot 25} - \sqrt{3 \cdot 25}$

$5 \sqrt{2} + 5 \cdot 3 \sqrt{2} - 5 \sqrt{3}$

$5 \sqrt{2} + 15 \sqrt{2} - 5 \sqrt{3}$

$20 \sqrt{2} - 5 \sqrt{3}$

Convert the numbers under the square root sign to two multiples. One of the multiples must be the square of a number.

Bring the square number out of the square root sign as its square root(e.g. 25 becomes 5) and multiply it by the coefficient. Collect like terms and work out the answer.