How do you simplify 2/(5- sqrt3)?

Feb 18, 2016

Multiply by the conjugate surd of the denominator.

$\frac{2}{5 - \sqrt{3}} = \frac{5 + \sqrt{3}}{11}$

Explanation:

The conjugate surd of $5 - \sqrt{3}$ is $5 + \sqrt{3}$.

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

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

$= \frac{2 \left(5 + \sqrt{3}\right)}{25 - 3}$

$= \frac{2 \left(5 + \sqrt{3}\right)}{22}$

$= \frac{5 + \sqrt{3}}{11}$