Question

Multiply 137592 by the smallest number so that the product is a perfect cube. Also, find the cube root of the product. [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 3 Marks

$137592=2\times 2\times 2\times 3\times 3\times 3\times 7\times 7\times 13$

The number 7 and 13 should be multiplied once and twice respectively so that the product is a perfect cube.

$\therefore$ The smalest number by which 137592 must be multiplied
$=7\times 13\times 13=1183$

The required product
$=137592\times 1183=2\times 2\times 2\times 3\times 3\times 3\times 7\times 7\times 13\times 7\times 13\times 13$

$=(2^3\times 3^3\times 7^3\times {13}^3)$

$=(2\times 3\times 7\times 13{)}^3$


$\sqrt[3]{3137592\times 1183}=2\times 3\times 7\times 13$

$=546$