Question

Освободите от иррациональности в знаменателе дроби 4/√10+√2

Answer 1

$frac{4}{sqrt{10} + sqrt{2} } = frac{4(sqrt{10} - sqrt{2})}{(sqrt{10} + sqrt{2})(sqrt{10} - sqrt{2}) }= frac{4(sqrt{10} - sqrt{2})}{(sqrt{10} )^{2} -( sqrt{2})^{2} }= frac{4(sqrt{10} - sqrt{2})}{10-2 }= frac{4(sqrt{10} - sqrt{2})}{8} }$$= frac{sqrt{10} - sqrt{2}}{2} }$