Question

Find the cube root of each of the following integers :

$\left(ii\right)-5832$

Answer 1

Step: Find the cube root of $-5832$

$\begin{array}{cc}\text{2}& \text{5832}\\ \text{2}& \text{2916}\\ \text{2}& \text{1458}\\ \text{3}& \text{729}\\ \text{3}& \text{243}\\ \text{3}& \text{81}\\ \text{3}& \text{27}\\ \text{3}& \text{9}\\ \text{3}& \text{3}\\ & \text{1}\end{array}$

$\sqrt[3]{3-5832}=-\sqrt[3]{35832}[\because \sqrt[3]{3-x}=-\sqrt[3]{3x}]$

Resolving $5832$ into prime factors
$5832=2\times 2\times 2\times 3\times 3\times 3\times 3\times 3\times 3$

Now, by grouping the factors into
the triplets of equal factors, we get,

$5832=(2\times 2\times 2)\times (3\times 3\times 3)\times (3\times 3\times 3)$

$\therefore \sqrt[3]{35832}=2\times 3\times 3=18$
$\therefore \sqrt[3]{3-5832}=-18$

Hence, the cube root of $-5832$ is $-18$.