# How do you rationalize 2/(5- sqrt 3)?

May 11, 2015

Try multiplying the numerator (top) and denominator (bottom) by the conjugate, $\left(5 + \sqrt{3}\right)$ :

2/(5-sqrt(3)) = (2(5+sqrt(3)))/((5-sqrt(3))(5+sqrt(3))

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

$= \frac{10 + 2 \sqrt{3}}{25 - 3}$

$= \frac{10 + 2 \sqrt{3}}{22}$

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

This is based on the equation:

$\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$