Question

Rationalise the denominators of the following:

(i) $\frac{1 }{ \sqrt{7 }}$

(ii) $\frac{1 }{ \sqrt{7 }-\sqrt6}$

(iii) $\frac{1 }{ \sqrt{5}+\sqrt2}$

(iv) $\frac{1 }{ \sqrt{7}-2}$

Answer 1

**(i) **$\frac{1 }{ \sqrt{7 }}$ =$\frac{1}{\sqrt7}=\frac{1}{\sqrt7} ×\frac{ √7 }{√7}$

= $\frac{ √7 }{√7}$

(ii) $\frac{1 }{ \sqrt{7 }-\sqrt6}$

$= \frac{1}{ (√7 + √6)} ×\frac{(√7 - √6)}{(√7 + √6)}$

= $\frac{(√7 - √6)}{7 - 6}=\sqrt7+\sqrt6$

**(iii) **$\frac{1 }{ \sqrt{7}-2}$

$\frac{\sqrt5+\sqrt2}{3}$

(iv) $\frac{1 }{ \sqrt{7}-2}$

$=\frac{\sqrt7+2}{7-2}=\frac{\sqrt7+2}{3}$