Question

Divide the number 26244 by the smallest number so that the quotient is a perfect cube. Also, find the cube root of the quotient. [4 MARKS]

Answer 1

Concept: 1 Mark
Applicaiton: 3 Marks

$26244=2\times 2\times 3\times 3\times 3\times 3\times 3\times 3\times 3\times 3$

Here $2\times 2$ and $3\times 3$ requires one more 2 and 3, to be grouped of three. Hence, the smallest number by which the given number must be divided in order that the quotient is a perfect cube is $2\times 2\times 3\times 3=36$

$\begin{array}{cc}2& 26244\\ 2& 13122\\ 3& 6561\\ 3& 2187\\ 3& 729\\ 3& 243\\ 3& 81\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$

$\therefore$ Quotient $=\frac{26244}{36}=729$

$=3\times 3\times 3\times 3\times 3\times 3$

$\therefore \sqrt[3]{3729}=3\times 3=9$