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# Rationalise the denominators of the following: (ii) 1 upon square root 7 minus square root 6

5. Rationalise the denominators of the following:

(ii)     $\frac{1}{\sqrt{7}-\sqrt{6}}$

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Given number is  $\frac{1}{\sqrt{7}-\sqrt{6}}$

Now, on rationalisation, we will get

$\Rightarrow \frac{1}{\sqrt 7-\sqrt6} = \frac{1}{\sqrt 7-\sqrt 6}\times \frac{\sqrt 7+\sqrt 6 }{\sqrt 7+\sqrt 6 } = \frac{\sqrt7+\sqrt 6}{(\sqrt7)^2-(\sqrt6)^2} = \frac{\sqrt7+\sqrt6}{7-6}$ $= \sqrt7+\sqrt6$

Therefore, the answer is  $\sqrt7+\sqrt6$

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