Question

Rationalise the denominator of each of the following:
$\frac{3-2\sqrt{2}}{3+2\sqrt{2}}$

Answer 1

On multiplying the numerator and denominator of the given number by $3-2\sqrt{2}$, we get:
$$\begin{gathered} \frac{3-2\sqrt{2}}{3+2\sqrt{2}}=\frac{3-2\sqrt{2}}{3+2\sqrt{2}}\times \frac{3-2\sqrt{2}}{3-2\sqrt{2}} \\ =\frac{{\left(3-2\sqrt{2}\right)}^2}{{\left(3\right)}^2-{\left(2\sqrt{2}\right)}^2} \\ =\frac{9+8-12\sqrt{2}}{9-8} \\ =17-12\sqrt{2} \end{gathered}$$