Question

$(sqrt{2frac{2}{5} }- sqrt{5frac{2}{5} }): sqrt{frac{3}{125} }$

Answer 1

$left (sqrt{2frac{2}{5}}- sqrt{5frac{2}{5}}right ):sqrt{frac{3}{125}}=left (sqrt{frac{12}{5}}-sqrt{frac{27}{5}}right )cdot sqrt{frac{125}{3}}=\\=left (frac{sqrt{3cdot 4}-sqrt{3^3}}{sqrt5}right )cdot sqrt{frac{5^3}{3}}=frac{sqrt3(sqrt4-sqrt{3^2})cdot sqrt{5^2}}{sqrt3}=frac{sqrt3(2-3)cdot 5}{sqrt3}=-1cdot 5=-5$