# How do you simplify 3/ (6- sqrt 5)?

Mar 13, 2018

$\frac{3}{6 - \sqrt{5}} = \frac{3}{31} \left(6 + \sqrt{5}\right)$

#### Explanation:

By rationalizing the denominator:

$\frac{3}{6 - \sqrt{5}} \times \frac{6 + \sqrt{5}}{6 + \sqrt{5}}$

$= \frac{3 \times \left(6 + \sqrt{5}\right)}{{6}^{2} - {\left(\sqrt{5}\right)}^{2}}$

$= \frac{3 \times \left(6 + \sqrt{5}\right)}{36 - 5}$

$= \frac{3}{31} \left(6 + \sqrt{5}\right)$

Mar 13, 2018

Multiply the numerator and denominator by the conjugate of the denominator and simplify

#### Explanation:

$\frac{3}{6 - \sqrt{5}}$
$\textcolor{w h i t e}{\text{XXX}} = \frac{3}{6 - \sqrt{5}} \cdot \frac{6 + \sqrt{5}}{6 + \sqrt{5}}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{3 \left(6 + \sqrt{5}\right)}{{6}^{2} - {\left(\sqrt{5}\right)}^{2}}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{18 + 3 \sqrt{5}}{36 - 5}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{18 + 3 \sqrt{5}}{31}$