# How do you rationalize x/(sqrt5-sqrt2)?

May 21, 2015

You can rationalize the denominator of this expression, by multiplying the numerator (top) and denominator (bottom) by the conjugate of $\sqrt{5} - \sqrt{2}$, namely $\sqrt{5} + \sqrt{2}$.

$\frac{x}{\sqrt{5} - \sqrt{2}}$

$= \frac{\left(\sqrt{5} + \sqrt{2}\right) x}{\left(\sqrt{5} + \sqrt{2}\right) \left(\sqrt{5} - \sqrt{2}\right)}$

$= \frac{\left(\sqrt{5} + \sqrt{2}\right) x}{\sqrt{5} \sqrt{5} - \sqrt{2} \sqrt{2}}$

$= \frac{\left(\sqrt{5} + \sqrt{2}\right) x}{5 - 2}$

$= \frac{\left(\sqrt{5} + \sqrt{2}\right) x}{3}$