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Properties of Conjugate of a Complex Number

Solve : 1√3...

Question

Solve : $\frac{1}{\sqrt{3} + \sqrt{2}} + \frac{1}{\sqrt{4} + \sqrt{3}} + \sqrt{2}$

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Solution

$\frac{1}{\sqrt{3} + \sqrt{2}} + \frac{1}{\sqrt{4} + \sqrt{3}} + \sqrt{2} = \frac{1}{\sqrt{3} + \sqrt{2}} \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}} + \frac{1}{\sqrt{4} + \sqrt{3}} \frac{\sqrt{4} - \sqrt{3}}{\sqrt{4} - \sqrt{3}} + \sqrt{2} = \sqrt{3} - \sqrt{2} + \sqrt{4} - \sqrt{3} + \sqrt{2} = \sqrt{4} = 2$

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