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# Rationalise the denominators of the following: (iv) 1 upon square root - 2

Q 5.     Rationalise the denominators of the following:

(iv)     $\frac{1}{\sqrt{7}-2}$

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Given number is  $\frac{1}{\sqrt{7}-2}$

Now, on rationalisation we will get

$\Rightarrow \frac{1}{\sqrt 7-2} = \frac{1}{\sqrt 7- 2}\times \frac{\sqrt 7+ 2 }{\sqrt 7+ 2 } = \frac{\sqrt7+ 2}{(\sqrt7)^2-(2)^2} = \frac{\sqrt7+2}{7-4}$
$= \frac{\sqrt7+2}{3}$

Therefore, answer is  $\frac{\sqrt7+2}{3}$

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