Question

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

iv) $1.331$

Answer 1

Step: Find the cube root of $1.331$

$1.331=\frac{1331}{1000}$

$\sqrt[3]{31.331}=\sqrt[3]{3\frac{1331}{1000}}$

$=\frac{\sqrt[3]{31331}}{\sqrt[3]{31000}}$ $[\because \sqrt[3]{3\frac{a}{b}}=\frac{\sqrt[3]{3a}}{\sqrt[3]{3b}}]$

$\begin{array}{cc}\text{11}& \text{1331}\\ \text{11}& \text{121}\\ \text{11}& \text{11}\\ & \text{1}\end{array}$

$=\frac{\sqrt[3]{3(11\times 11\times 11)}}{\sqrt[3]{310\times 10\times 10}}$

$=\frac{11}{10}$

$=1.1$

Hence, the cube root of $1.331$ is $1.1$.