# How do you rationalize the denominator (8sqrt2)/(sqrt20-sqrt18)?

May 27, 2015

To rationalize the denominator, multiply both the numerator and the denominator by the conjugate of the denominator.

$\frac{8 \sqrt{2}}{\sqrt{20} - \sqrt{18}}$

$= \frac{8 \sqrt{2}}{\sqrt{20} - \sqrt{18}} \cdot \frac{\sqrt{20} + \sqrt{18}}{\sqrt{20} + \sqrt{18}}$

$= \frac{8 \sqrt{40} + 8 \sqrt{36}}{20 - 18}$

$= \frac{8 \left(2 \sqrt{10} + 6\right)}{2}$

$= 24 + 8 \sqrt{10}$