# How do you rationalize the denominator (8sqrt2)/(2sqrt5-3sqrt2)?

Jun 14, 2015

Multiply both numerator and denominator by the conjugate $\left(2 \sqrt{5} + 3 \sqrt{2}\right)$ to get:

$\frac{8 \sqrt{2}}{2 \sqrt{5} - 3 \sqrt{2}} =$

#### Explanation:

$\frac{8 \sqrt{2}}{2 \sqrt{5} - 3 \sqrt{2}}$

$= \frac{8 \sqrt{2}}{2 \sqrt{5} - 3 \sqrt{2}} \cdot \frac{2 \sqrt{5} + 3 \sqrt{2}}{2 \sqrt{5} + 3 \sqrt{2}}$

$= \frac{8 \sqrt{2} \left(2 \sqrt{5} + 3 \sqrt{2}\right)}{20 - 18}$

$= 4 \sqrt{2} \left(2 \sqrt{5} + 3 \sqrt{2}\right)$

$= 8 \sqrt{2} \sqrt{5} + 24$

$= 8 \sqrt{10} + 24$

$= 8 \left(\sqrt{10} + 3\right)$