Question

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

Answer 1

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

$\frac{3\sqrt{3}+1}{2\sqrt{5}-3}\times \frac{2\sqrt{5}+3}{2\sqrt{5}+3}$

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

$=\frac{6\sqrt{15}+9\sqrt{3}+2\sqrt{5}+3}{20-3}$

$=\frac{6\sqrt{15}+9\sqrt{3}+2\sqrt{5}+3}{17}$