Question

Rational the denominator & simplify:-
$\frac{30}{5\sqrt{3}-3\sqrt{5}}$

Answer 1

Rationalizing the denominator of $\frac{30}{5\sqrt{3}-3\sqrt{5}}$.

$\frac{30}{5\sqrt{3}-3\sqrt{5}}\times \frac{\left(5\sqrt{3}+3\sqrt{5}\right)}{\left(5\sqrt{3}+3\sqrt{5}\right)}$

$=\frac{30\left(5\sqrt{3}+3\sqrt{5}\right)}{{\left(5\sqrt{3}\right)}^2-{\left(3\sqrt{5}\right)}^2}$

$=\frac{30\left(5\sqrt{3}+3\sqrt{5}\right)}{75-45}$

$=\frac{30\left(5\sqrt{3}+3\sqrt{5}\right)}{30}$

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