Question

simplify 1/root3+root2-root5​

Answer 1

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