Question

Освободитесь от иррациональности в знаменателе: $frac{8}{sqrt{6}+sqrt{2}}$

Answer 1

$frac{8}{sqrt{6}+sqrt{2}}=frac{8(sqrt{6}-sqrt{2})  }{(sqrt{6}+sqrt{2})(sqrt{6} -sqrt{2}) } = frac{8(sqrt{6}-sqrt{2}) }{6-2} =2(sqrt{6}-sqrt{2})$

Answer 2

$frac{8}{ sqrt{6} + sqrt{2} } = frac{8 times ( sqrt{6} - sqrt{2} )}{( sqrt{6} + sqrt{2} )( sqrt{6} - sqrt{2} )} = \ frac{8( sqrt{6} - sqrt{2} )}{ 6 - 2} = frac{8( sqrt{6} - sqrt{2} )}{4} = \ 2( sqrt{6} - sqrt{2} ) = 2 sqrt{6} - 2 sqrt{2}$