# How do you rationalise the denominator of 8/(3-sqrt5)?

Apr 3, 2016

Multiply both numerator and denominator by $3 + \sqrt{5}$ and simplify.

#### Explanation:

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

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

$= \frac{24 + 8 \sqrt{5}}{{3}^{2} - {\left(\sqrt{5}\right)}^{2}}$

$= \frac{24 + 8 \sqrt{5}}{9 - 5}$

$= \frac{24 + 8 \sqrt{5}}{4}$

$= 6 + 2 \sqrt{5}$

The expression $\left(3 + \sqrt{5}\right)$ is called the conjugate of $\left(3 - \sqrt{5}\right)$