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# Rationalise the denominators of the following: (iii)

5. Rationalise the denominators of the following:

(iii)     $\frac{1}{\sqrt{5}+\sqrt{2}}$

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Given number is  $\frac{1}{\sqrt{5}+\sqrt{2}}$

Now, on rationalisation, we will get

$\\= \frac{1}{\sqrt 5+\sqrt2} \\\\= \frac{1}{\sqrt 5+\sqrt 2}\times \frac{\sqrt 5-\sqrt 2 }{\sqrt 5-\sqrt 2 }\\\\ = \frac{\sqrt5-\sqrt 2}{(\sqrt5)^2-(\sqrt2)^2} \\\\= \frac{\sqrt5-\sqrt2}{5-2}$
$= \frac{\sqrt5-\sqrt2}{3}$

Therefore, the answer is  $\frac{\sqrt5-\sqrt2}{3}$

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