Question

Найди значение выражения (√2 2/5−√5 2/5)÷√3/125

Answer 1

$displaystyle (sqrt{2frac{2}{5}}-sqrt{5frac{2}{5}}):sqrt{frac{3}{125}}=(sqrt{frac{12}{5}}-sqrt{frac{27}{5}}):sqrt{frac{3}{125}}= \\ =sqrt{frac{12}{5}}:sqrt{frac{3}{125}}-sqrt{frac{27}{5}}:sqrt{frac{3}{125}}=sqrt{frac{12}{5}:frac{3}{125}}-sqrt{frac{27}{5}:frac{3}{125}}= \\ =sqrt{frac{12}{5}*frac{125}{3}}-sqrt{frac{27}{5}*frac{125}{3}}=sqrt{4*25}-sqrt{9*25}=sqrt{4}*sqrt{25}-sqrt{9}*sqrt{25}= \\ =(sqrt{4}-sqrt{9})*sqrt{25}=(2-3)*5=(-1)*5=-5$