# How do you rationalize the denominator and simplify 3/(6-sqrt5)?

Apr 4, 2016

$\frac{18}{31} + \frac{3}{31} \sqrt{5}$

#### Explanation:

WE can rationalize the denominator in $\frac{3}{6 - \sqrt{5}}$ by multiplying numerator and denominator by conjugate of the denominator. The conjugate of $\left(6 - \sqrt{5}\right)$ is $\left(6 + \sqrt{5}\right)$.

Hence $\frac{3}{6 - \sqrt{5}} = \frac{3 \cdot \left(6 + \sqrt{5}\right)}{\left(6 - \sqrt{5}\right) \left(6 + \sqrt{5}\right)}$

= $\frac{18 + 3 \sqrt{5}}{36 - 5}$ or

= $\frac{18}{31} + \frac{3}{31} \sqrt{5}$