# How do you rationalize the denominator of sqrt(2)/(sqrt(3)-4)?

Apr 3, 2018

$\frac{\sqrt{6} + 4 \sqrt{2}}{-} 13$

#### Explanation:

When rationalising the denominator, you just need to times both the numerator and denominator by the conjugate of the denominator

The purpose of rationalising the denominator is so that you get a rational number for your denominator

$\frac{\sqrt{2}}{\left(\sqrt{3}\right) - 4}$
= sqrt2/((sqrt3)-4)times (sqrt3+4)/((sqrt3+4)
= $\frac{\sqrt{6} + 4 \sqrt{2}}{3 - 16}$
=$\frac{\sqrt{6} + 4 \sqrt{2}}{-} 13$