# How do you rationalize the denominator and simplify sqrt(10)/(sqrt(5)-2)?

May 28, 2017

I got as far as this:

#### Explanation:

Multiply and divide by $\sqrt{5} + 2$:

$\frac{\sqrt{10}}{\sqrt{5} - 2} \cdot \frac{\sqrt{5} + 2}{\sqrt{5} + 2} =$

$= \sqrt{10} \cdot \frac{\sqrt{5} + 2}{5 - 4} = \sqrt{5 \cdot 2} \cdot \frac{\sqrt{5} + 2}{1} =$

$= \sqrt{5} \sqrt{2} \cdot \left[\sqrt{5} + 2\right] = 5 \sqrt{2} + 2 \sqrt{5} \sqrt{2} =$

$= \sqrt{2} \left[5 + 2 \sqrt{5}\right]$