Question

Find the cube root of each of the following numbers:

(ii) $-1728\times 216$

Answer 1

Step: Find the cube root of $-1728\times 216$

Cube root of $-1728\times 216=\sqrt[3]{3-1728\times 216}$

$\because \sqrt[3]{3a\times b}=\sqrt[3]{3a}\times \sqrt[3]{3b}$

$\therefore \sqrt[3]{3-1728\times 216}$

$=\sqrt[3]{3-1728}\times \sqrt[3]{3216}$

$=-\sqrt[3]{31728}\times \sqrt[3]{3216}$ $[\because \sqrt[3]{3-a}=-\sqrt[3]{3a}]$

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


$=-\sqrt[3]{32\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3}\times \sqrt[3]{36\times 6\times 6}$

$=-2\times 2\times 3\times 6$

$=-72$

Hence, the cube root of $-1728\times 216$
is $-72$.