How do you simplify (sqrt10 - sqrt 5) /( sqrt 10 + sqrt 5)?

Aug 11, 2016

$= 3 - 2 \sqrt{2}$

Explanation:

$\frac{\sqrt{10} - \sqrt{5}}{\sqrt{10} + \sqrt{5}}$
Multiplying both the sides by $\sqrt{10} - \sqrt{5}$
We get
${\left(\sqrt{10} - \sqrt{5}\right)}^{2} / \left(\left(\sqrt{10} + \sqrt{5}\right) \left(\sqrt{10} - \sqrt{5}\right)\right)$
$= \frac{10 + 5 - 2 \times \sqrt{10} \times \sqrt{5}}{10 - 5}$
$= \frac{15 - 10 \sqrt{2}}{5}$
$= 5 \frac{3 - 2 \sqrt{2}}{5}$
$= 3 - 2 \sqrt{2}$