Question

Find the cube root of each of the following integers :

$\left(iii\right)-2744000$

Answer 1

Step : Find the cube root of $-2744000$

$\begin{array}{cc}\text{2}& \text{2744}\\ \text{2}& \text{1372}\\ \text{2}& \text{686}\\ \text{7}& \text{343}\\ \text{7}& \text{49}\\ \text{7}& \text{7}\\ & \text{1}\end{array}$

$\sqrt[3]{3-2744000}=-\sqrt[3]{32744000}[\because \sqrt[3]{3-x}=-\sqrt[3]{3x}]$
$=-\sqrt[3]{32744\times 1000}$
$=-\sqrt[3]{32\times 2\times 2\times 7\times 7\times 7\times 10\times 10\times 10}$
$=-(2\times 7\times 10)$
$=-140$

Hence, the cube root of $-2744000$ is $-140$