Question:
Rationalisation of the denominator of $\frac{1}{\sqrt{5}+\sqrt{2}}$ gives
(a) $\frac{1}{\sqrt{10}}$
(b) $\sqrt{5}+\sqrt{2}$
(c) $\sqrt{5}-\sqrt{2}$
(d) $\frac{\sqrt{5}-\sqrt{2}}{3}$
Solution:
$\frac{1}{\sqrt{5}+\sqrt{2}}$
Rationalisation of denominator gives
$\frac{1}{\sqrt{5}+\sqrt{2}} \times \frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}-\sqrt{2}}=\frac{\sqrt{5}-\sqrt{2}}{5-2}=\frac{\sqrt{5}-\sqrt{2}}{3}$
Hence, the correct answer is option (d).
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