Question

By what smallest number should we divide $9000$ so that the quotient becomes a perfect cube. Find the cube root of the quotient

• A. 9, 10
• B. 9, 1
• C. 19, 10
• D. 19, 5

Answer 1

The correct option is A. $9,10$

Given $9000=3\times 3\times 10\times 10\times 10$

$\Rightarrow 9000={10}^3\times 3^2$

To make it a perfect cube, we need to have $3$ multiples of prime factors but here its $3^2$ which is not a perfect cube. So, we divide the number by $3^2=9$

New number $=\frac{{10}^3\times 3^2}{3^2}$
$={10}^3$
$=1000$

And also $\sqrt[3]{31000}=10$