Question

rationalize 2√2/√3+√5

Answer 1

$\frac{2 \sqrt{2} }{ \sqrt{3} + \sqrt{5} } \\ = \frac{2 \sqrt{2}( \sqrt{3} - \sqrt{5}) }{ (\sqrt{3} + \sqrt{5} )( \sqrt{3} - \sqrt{5}) } \\ = \frac{2 \sqrt{6} - 2 \sqrt{10} }{( { \sqrt{3}) }^{2} - ( { \sqrt{5}) }^{2} } \\ \frac{2 \sqrt{6} - 2 \sqrt{10} }{3 - 5} \\ = \frac{2( \sqrt{6} - \sqrt{10} ) }{ - 2} \\ = \sqrt{10} - \sqrt{6}$