Question

Fill in the blanks :

vii) $\sqrt[3]{3\frac{27}{125}}=\frac{\cdots }{5}$

Answer 1

Step: Fill in the blank

Given: $\sqrt[3]{3\frac{27}{125}}=\frac{\cdots }{5}$

$\sqrt[3]{3\frac{27}{125}}=\frac{\sqrt[3]{327}}{\sqrt[3]{3125}}$ $(\because \sqrt[3]{3\frac{a}{b}}=\frac{\sqrt[3]{3a}}{\sqrt[3]{3b}})$
$=\frac{\sqrt[3]{33\times 3\times 3}}{\sqrt[3]{35\times 5\times 5}}$
$=\frac{3}{5}$

Hence, the correct answer is $3$.