# What is the Square root of 20 - square root of 45 + 2 square root of 125?

Sep 19, 2015

$\sqrt{20} - \sqrt{45} + 2 \sqrt{125} = 9 \sqrt{5}$

#### Explanation:

Use prime factorization to make it easier findthe perfect squares that can be taken out from the radical sign.

$\sqrt{20} - \sqrt{45} + 2 \sqrt{125}$ can be factorized to:

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

Then, take out the perfect squares and simplify them:

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

Finally, add the terms together to get the solution:

$2 \sqrt{5} - 3 \sqrt{5} + 10 \sqrt{5} = 9 \sqrt{5}$