Question

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

i) $0.001728$

Answer 1

Step: Find the cube root of $0.001728$

$0.001728=\frac{1728}{1000000}$

$\sqrt[3]{30.001728}=\sqrt[3]{3\frac{1728}{1000000}}$

$=\frac{\sqrt[3]{31728}}{\sqrt[3]{31000000}}$ $[\because \sqrt[3]{3\frac{a}{b}}=\frac{\sqrt[3]{3a}}{\sqrt[3]{3b}}]$

$\begin{array}{cc}\text{2}& \text{1728}\\ \text{2}& \text{864}\\ \text{2}& \text{432}\\ \text{2}& \text{216}\\ \text{2}& \text{108}\\ \text{2}& \text{54}\\ \text{3}& \text{27}\\ \text{3}& \text{9}\\ \text{3}& \text{3}\\ & \text{1}\end{array}$


$=\frac{\sqrt[3]{3(2\times 2\times 2)\times (2\times 2\times 2)\times (3\times 3\times 3)}}{\sqrt[3]{3100\times 100\times 100}}$

$=\frac{2\times 2\times 3}{100}$

$=\frac{12}{100}$

$=0.12$

Hence, the cube root of $0.001728$
is $0.12$.