# How do you simplify (sqrt 3 -sqrt 6) / (sqrt 3 +sqrt6)?

##### 1 Answer
Feb 10, 2016

$= - 3 + 2 \sqrt{2}$

#### Explanation:

When you have a sum of two square roots, the trick is to multiply by the equivalent subtraction:

$\frac{\sqrt{3} - \sqrt{6}}{\sqrt{3} + \sqrt{6}}$

$= \frac{\sqrt{3} - \sqrt{6}}{\sqrt{3} + \sqrt{6}} \cdot \frac{\sqrt{3} - \sqrt{6}}{\sqrt{3} - \sqrt{6}} =$

=((sqrt(3))^2-2*sqrt(3)*sqrt(6)+(sqrt(6))^2)/((sqrt(3))^2-(sqrt(6))^2

$= \frac{3 - 2 \sqrt{18} + 6}{3 - 6}$

$= \frac{9 - 2 \cdot \sqrt{9 \cdot 2}}{-} 3$

$= \frac{9 - 2 \cdot 3 \sqrt{2}}{-} 3$

$= - 3 + 2 \sqrt{2}$