# Question #30bd9

Nov 7, 2017

$6 \sqrt{2} - 6 \sqrt{3} + \sqrt{5}$

#### Explanation:

$6 \sqrt{2} - 20 \frac{\sqrt{1}}{\sqrt{5}} - \sqrt{108} + \sqrt{125}$

First you mus get rid of the sqrt in the numerator:

$6 \sqrt{2} - 4 \cdot 5 \cdot \left(\frac{1}{\sqrt{5}}\right) - \sqrt{108} + \sqrt{125}$

$6 \sqrt{2} - 4 \sqrt{5} - \sqrt{108} + \sqrt{125}$

Then decompose the larger number in prime factors:

$6 \sqrt{2} - 4 \sqrt{5} - \sqrt{{2}^{2} \cdot {3}^{3}} + \sqrt{{5}^{3}}$

Knownig that $\sqrt{{a}^{2}} = a$ we can do this:

$6 \sqrt{2} - 4 \sqrt{5} - 2 \cdot 3 \sqrt{3} + 5 \sqrt{5}$

Simplifing gives:

$6 \sqrt{2} - 6 \sqrt{3} + \sqrt{5}$