Question

Упростите $sqrt{ frac{2}{5} }+ sqrt{ frac{5}{2} }+ sqrt{10}$

Answer 1

$sqrtfrac{2}{5} + sqrtfrac{5}{2}+ sqrt{10}= sqrtfrac{4}{10}+ sqrtfrac{25}{10}+ sqrt{10}= frac{2}{ sqrt{10} } + frac{5}{sqrt{10}}+sqrt{10}=\\= frac{2+5}{sqrt{10}} +sqrt{10}= frac{7}{sqrt{10}}+sqrt{10}= frac{7+10}{sqrt{10}}= frac{17}sqrt{10}}= frac{17sqrt{10}}{10}=1,7sqrt{10}$