Question

Guys please solve this. ​

Answer 1

it is ur answer

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Answer 2

Answer:

$\frac{1}{ \sqrt{2} + \sqrt{3} + \sqrt{5} }$ [Given]

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

On rationalising the denominator;

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

$= \frac{ \sqrt{2} + \sqrt{3} - \sqrt{5} }{2 + 3 + 2 \sqrt{6} - 5}$

$= \frac{ \sqrt{2} + \sqrt{3} - \sqrt{5} }{2 \sqrt{6} }$

On rationalising the denominator:

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

$= \frac{2 \sqrt{12} + 2 \sqrt{18} - 2 \sqrt{30} }{4 \times 6}$

$= \frac{4 \sqrt{3} + 6 \sqrt{2} - 2 \sqrt{30} }{24}$

$= \frac{2 \sqrt{3} + 3 \sqrt{2} - \sqrt{30} }{12}$