Question

Find the cube root of each of the following integers :

$\left(i\right)-125$

Answer 1

Step : Find the cube root of $-125$

$\begin{array}{cc}\text{5}& \text{125}\\ \text{5}& \text{25}\\ \text{5}& \text{5}\\ & \text{1}\end{array}$

$\sqrt[3]{3-125}=-\sqrt[3]{3125}[\because \sqrt[3]{3-x}=-\sqrt[3]{3x}]$
Resolving $125$ into prime factors
$125=5\times 5\times 5$
$\therefore \sqrt[3]{3125}=5$
$\Rightarrow \sqrt[3]{3-125}=-5$

Hence, the cube root of $-125$ is $-5$ .