Rationalise $\frac{1}{\sqrt{3} + \sqrt{2}}$

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Solution

$\frac{1}{\sqrt{3} + \sqrt{2}} = \frac{1 (\sqrt{3} - \sqrt{2})}{(\sqrt{3} + \sqrt{2}) (\sqrt{3} - \sqrt{2})} = \frac{\sqrt{3} - \sqrt{2}}{3 - 2} = \sqrt{3} - \sqrt{2}$

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