# What is the simplified form of square root of 10 - square root of 5 over square root of 10 + square root of 5?

Sep 12, 2015

(sqrt(10)-sqrt(5))/(sqrt(10)+sqrt(5)=3-2sqrt(2)

#### Explanation:

(sqrt(10)-sqrt(5))/(sqrt(10)+sqrt(5)
$\textcolor{w h i t e}{\text{XXX}} = \frac{\cancel{\sqrt{5}}}{\cancel{\sqrt{5}}} \cdot \frac{\sqrt{2} - 1}{\sqrt{2} + 1}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{\sqrt{2} - 1}{\sqrt{2} + 1} \cdot \frac{\sqrt{2} - 1}{\sqrt{2} - 1}$

color(white)("XXX")=(sqrt(2)-1)^2/((sqrt(2)^2-1^2)

$\textcolor{w h i t e}{\text{XXX}} = \frac{2 - 2 \sqrt{2} + 1}{2 - 1}$

$\textcolor{w h i t e}{\text{XXX}} = 3 - 2 \sqrt{2}$