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

Apr 9, 2017

$- \frac{\sqrt{10}}{3}$

#### Explanation:

Multiply the surd conjugate to get rid of $\sqrt{2}$ .

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

$= \frac{- 2 \sqrt{10}}{3 \cdot 2}$

$= \frac{- 2 \sqrt{10}}{6}$

$- \frac{2}{6}$ can be simplified to $- \frac{1}{3}$

$= - \frac{\sqrt{10}}{3}$