Question

Find the cube root of each of the following numbers:

(iii) $-27\times 2744$

Answer 1

Step: Find the cube root of $-27\times 2744$

Cube root of $-27\times 2744=\sqrt[3]{3-27\times 2744}$

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

$\therefore \sqrt[3]{3-27\times 2744}$

$=\sqrt[3]{3-27}\times \sqrt[3]{32744}$

$=-\sqrt[3]{327}\times \sqrt[3]{32744}$ $[\because \sqrt[3]{3-a}=-\sqrt[3]{3a}]$

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

$=-\sqrt[3]{33\times 3\times 3}\times \sqrt[3]{32\times 2\times 2\times 7\times 7\times 7}$

$=-3\times 2\times 7$

$=-42$

Hence, the cube root of $-27\times 2744$
is $-42$.