Question

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

Answer 1

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

Answer 2

Для удобства вычислений заметим, что √2 = (√2/5)^2 и √5 = (√5/5)^2, тогда:

(√2 2/5−√5 2/5)÷√3/125 = [(√2/5)^2 2/5 - (√5/5)^2 2/5] ÷ (1/5√3)^2

= [(2/25)(√2/5)^2 - (2/25)(√5/5)^2] ÷ (1/25)(1/3)

= (2/25) [(2/5) - (1/5)] × 75

= (2/25) × (1/5) × 75

= 6

Таким образом, значение выражения равно 6.