Question

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

ii) $0.003375$

Answer 1

Step: Find the cube root of $0.003375$

$0.003375=\frac{3375}{1000000}$

$\sqrt[3]{30.003375}=\sqrt[3]{3\frac{3375}{1000000}}$

$=\frac{\sqrt[3]{33375}}{\sqrt[3]{31000000}}$ $[\because \sqrt[3]{3\frac{a}{b}}=\frac{\sqrt[3]{3a}}{\sqrt[3]{3b}}]$

$\begin{array}{cc}\text{5}& \text{3375}\\ \text{5}& \text{675}\\ \text{5}& \text{135}\\ \text{3}& \text{27}\\ \text{3}& \text{9}\\ \text{3}& \text{3}\\ & \text{1}\end{array}$


$=\frac{\sqrt[3]{3(5\times 5\times 5)\times (3\times 3\times 3)}}{\sqrt[3]{3100\times 100\times 100}}$

$=\frac{5\times 3}{100}$

$=\frac{15}{100}$

$=0.15$

Hence, the cube root of $0.003375$
is $0.15$.