Question

Rationalise the following:
i) 1/5√3
ii) 1/√7
iii) 1/3+√2

Answer 1

$i) \: \frac{1}{5 \sqrt{3} }$

on rationalisation

$\frac{1}{5 \sqrt{3} } \times \frac{5 \sqrt{3} }{5 \sqrt{3} }$

$\frac{5 \sqrt{3} }{25 \times 3} \\ \\ = \frac{5 \sqrt{3} }{75}$

$ii) \: \frac{1}{ \sqrt{7} }$

on rationalisation

$\frac{1}{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} } \\ \\= \frac{ \sqrt{7} }{7}$

$iii) \: \frac{1}{3 + \sqrt{2} }$

on rationalisation

$\frac{1}{3 + \sqrt{2} } \times \frac{3 - \sqrt{2} }{3 - \sqrt{2} } \\ = \frac{3 - \sqrt{2} }{9 - 2 } \\ \\ = \frac{3 - \sqrt{2} }{7}$