Rationalise the denominators of the following:
(i) \(\frac{1 }{ \sqrt{7 }}\)
(ii) \(\frac{1 }{ \sqrt{7 }-\sqrt6}\)
(iii) \(\frac{1 }{ \sqrt{5}+\sqrt2}\)
(iv) \(\frac{1 }{ \sqrt{7}-2}\)
Rationalise the denominators of the following:
(i) \(\frac{1 }{ \sqrt{7 }}\)
(ii) \(\frac{1 }{ \sqrt{7 }-\sqrt6}\)
(iii) \(\frac{1 }{ \sqrt{5}+\sqrt2}\)
(iv) \(\frac{1 }{ \sqrt{7}-2}\)
Solution and Explanation
(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) \(\frac{1 }{ \sqrt{7}-2}\)
\(=\frac{\sqrt7+2}{7-2}=\frac{\sqrt7+2}{3}\)
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