Question

Find the cube root of each of the following rational numbers:

iii) $0.001$

Answer 1

Step: Find the cube root of $0.001$

$0.001=\frac{1}{1000}$

$\sqrt[3]{30.001}=\sqrt[3]{3\frac{1}{1000}}$

$=\frac{\sqrt[3]{31}}{\sqrt[3]{31000}}$ $[\because \sqrt[3]{3\frac{a}{b}}=\frac{\sqrt[3]{3a}}{\sqrt[3]{3b}}]$

$=\frac{1}{\sqrt[3]{310\times 10\times 10}}$

$=\frac{1}{10}$

$=0.1$

Hence, the cube root of $0.001$ is $0.1$.