Question

On multiplying $137592$ by the smallest number _____ the product is a perfect cube, the cube root of this perfect cube number is _____.

• A. $7\times {13}^2,546$
• B. $7\times {13}^3,546$
• C. $5\times 13,546$
• D. $7\times {13}^4,546$

Answer 1

Answer: (A)

$7\times {13}^2,546$

By prime factorization you can find out that
$137592=2^3\times 3^3\times 7^2\times 13$
For it to be perfect cube it should be multiplied by $7\times {13}^2$
Cube root of product $=\sqrt[3]{37\times {13}^2\times 137592}$
$\sqrt[3]{32^3\times 3^3\times 7^3\times {13}^3}$
$=2\times 3\times 7\times 13=546$