Question

Rational the denominator & simplify:-
$\frac{1}{2\sqrt{5}-\sqrt{3}}$

Answer 1

Rationalizing the denominator of $\frac{1}{2\sqrt{5}-\sqrt{3}}$.

$\frac{1}{2\sqrt{5}-\sqrt{3}}\times \frac{\left(2\sqrt{5}+\sqrt{3}\right)}{\left(2\sqrt{5}+\sqrt{3}\right)}$

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

$=\frac{2\sqrt{5}+\sqrt{3}}{20-3}$

$=\frac{2\sqrt{5}+\sqrt{3}}{17}$