# How do you rationalize the denominator 2/(5-sqrt3)?

Jun 3, 2015

$\frac{2}{5 - \sqrt{3}}$

We can ratioinalise the denominator by multiplying the numerator and denominator of the expression by the conjugate of $5 - \sqrt{3}$

The conjugate of 5-sqrt3 = color(red)(5+sqrt3

=(2xxcolor(red)((5+sqrt3)))/((5-sqrt3)xxcolor(red)((5+sqrt3))

We know that color(blue)((a-b)(a+b)=a^2 - b^2
so ,(5-sqrt3)xx(5+sqrt3) = 5^2- sqrt3^2 = color(blue)(25 - 3 = 22

the expression becomes:
$\frac{\cancel{2} \times \textcolor{red}{\left(5 + \sqrt{3}\right)}}{\cancel{22}}$

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