Question

Rationalize the denominator of $\frac{1}{5+\sqrt{3}}$.

Answer 1

The denominator is $5+\sqrt{3}$. Its conjugate is $5-\sqrt{3}$ or the rationalizing factor is $5-\sqrt{3}$.
$\frac{1}{5+\sqrt{3}}=\frac{1}{5+\sqrt{3}}\times \frac{5-\sqrt{3}}{5-\sqrt{3}}$
$=\frac{5-\sqrt{3}}{5^2-(\sqrt{3}{)}^2}=\frac{5-\sqrt{3}}{25-3}=\frac{5-\sqrt{3}}{22}$