Question

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

Answer 1

Multiplying and dividing the given expression by $5+3\sqrt{2}$:

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

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

$=\frac{25+18+30\sqrt{2}}{25-18}$

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