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

Mar 31, 2015

You first multiply top and bottom with $\sqrt{5} + 2$

This will give the special product ${A}^{2} - {B}^{2}$ as denominator

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

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

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

$= 5 \sqrt{2} + 2 \sqrt{10}$