On rationalizing the denominator of $\frac{1}{\sqrt{7} -\sqrt{6}}$, we get _____.

To do: Rationalize the following

Solution:

$\frac{1}{\sqrt{7} -\sqrt{6}}$

Multiply by $\sqrt{7} +\sqrt{6}$ on numerator and denominator

=$\frac{1}{\sqrt{7} -\sqrt{6}} \times \frac{\sqrt{7} +\sqrt{6}}{\sqrt{7} +\sqrt{6}}$

=$\frac{\sqrt{7} +\sqrt{6}}{\sqrt{7}^{2} -\sqrt{6}^{2}}$

=$\frac{\sqrt{7} +\sqrt{6}}{7-6}$

=$\frac{\sqrt{7} +\sqrt{6}}{1}$

=$\sqrt{7} +\sqrt{6}$

Therefore on rationalizing $\frac{1}{\sqrt{7} -\sqrt{6}}$ we get $\sqrt{7}+\sqrt{6}$

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Updated on: 10-Oct-2022

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