Question

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

Answer 1

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