Question

1/(root2+ root3+ root5)

Answer 1

Answer:

1/(√2+√3+√5)

1{(√2+√3)-(√5)}/(√2+√3)²-(√5)²

(√2+√3)-(√5)/(√2)²+(√3)²+2√6-(√5)²

√2+√3-√5/2+3-5+2√6

√2+√3-√5/2√6

√6(√2+√3-√5)/2×6

√12+√18-√30/12

Answer 2

Answer:

$\frac{1}{ \sqrt{3} + \sqrt{2} + \sqrt{5} } = \frac{3 \sqrt{2} + 2 \sqrt{3} - \sqrt{30} }{12}$

Explanation:

$\frac{1}{ \sqrt{2} + \sqrt{3} + \sqrt{5} }$

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

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

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

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

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

multiplying √6 in both

$\frac{ \sqrt{6}( \sqrt{3} + \sqrt{2} - \sqrt{5} )}{ \sqrt{6} \: \: \times \: \: 2 \sqrt{6} }$

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

THEREFORE

THE ANSWER IS :-

$\frac{1}{ \sqrt{3} + \sqrt{2} + \sqrt{5} } = \frac{3 \sqrt{2} + 2 \sqrt{3} - \sqrt{30} }{12}$