Question

Show that reciprocal of $3+2\surd 2$ is an irrational number

Answer 1

Reciprocol of $3+2\sqrt{2}$ is $=\frac{1}{3+2\sqrt{2}}$

On rationalisation, We get

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

$=\frac{3-2\sqrt{2}}{9-8}$

$=3-2\sqrt{2}$

which is an irrational number.