How do you rationalize  3 / (sqrt5 -sqrt2) ?

May 14, 2015

You can rationalize the denominator by multiplying top and bottom by the conjugate $\sqrt{5} + \sqrt{2}$ as follows:

$\frac{3}{\sqrt{5} - \sqrt{2}}$

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

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

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

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

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