Question

Rationalise the denominator of $\frac{5+3\sqrt{2}}{5-3\sqrt{2}}$

Answer 1

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

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

$\Rightarrow \frac{5^2+{\left(3\sqrt{2}\right)}^2+2\times 5\times 3\sqrt{2}}{25-18}$

$\Rightarrow \frac{25+18+30\sqrt{2}}{7}$

$\Rightarrow \frac{43+30\sqrt{2}}{7}$

$\Rightarrow \frac{1}{7}(43+30\sqrt{2})$

Hence, this is the answer.