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) \(\frac{1 }{ \sqrt{7}-2}\)

\(=\frac{\sqrt7+2}{7-2}=\frac{\sqrt7+2}{3}\)