Question

Rationalise the denominator of
$\frac{1}{ \sqrt{2} + \sqrt{3} + \sqrt{5} }$
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Answer 1

$\huge\mathfrak{Answer:-}$

$\frac{1}{ \sqrt{2} + \sqrt{3} + \sqrt{5} } \\ = \frac{1}{ \sqrt{2} + \sqrt{3} + \sqrt{5} } \times \frac{( \sqrt{2} + \sqrt{3} ) - \sqrt{5} }{( \sqrt{2} + \sqrt{3}) - \sqrt{5} } \\ = \frac{ \sqrt{2} + \sqrt{3} - \sqrt{5} }{ { (\sqrt{2} + \sqrt{3)} }^{2} - ( { \sqrt{5)} }^{2} } \\ = \frac{ \sqrt{2} + \sqrt{3} - \sqrt{5} }{2 + 3 + 2 \sqrt{6} - 5 } \\ = \frac{ \sqrt{2} + \sqrt{3} - \sqrt{5} }{2 \sqrt{6} }$