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Rationalisation

Find the valu...

Question

Find the value of $\frac{1}{\sqrt{5} - \sqrt{5 - \sqrt{24}}} + \frac{1}{\sqrt{5} - \sqrt{5 + \sqrt{24}}}$ .

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Solution

Now,
$\frac{1}{\sqrt{5} - \sqrt{5 - \sqrt{24}}} + \frac{1}{\sqrt{5} - \sqrt{5 + \sqrt{24}}}$

Let's rationalize the denominator of both the terms, we get

$= \frac{\sqrt{5} + \sqrt{5 - \sqrt{24}}}{(\sqrt{5})^{2} - (\sqrt{5 - \sqrt{24}})^{2}} + \frac{\sqrt{5} + \sqrt{5 + \sqrt{24}}}{(\sqrt{5})^{2} - (\sqrt{5 + \sqrt{24}})^{2}}$

$= \frac{1}{24} (\sqrt{5} + \sqrt{5 - \sqrt{24}} - \sqrt{5} - \sqrt{5 + \sqrt{24}})$

$= \frac{1}{24} (\sqrt{5 - \sqrt{24}} - \sqrt{5 + \sqrt{24}})$

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