Question

Find the smallest number which when multiplied with $3600$ will make the product a perfect cube. Further, find the cube root of the product.

• A. $60,60$
• B. $60,6$
• C. $6,6$
• D. $6,60$

Answer 1

Answer: (A)

The correct option is A $60,60$

Prime factorising $3600$, we get,

$3600=3\times 3\times 2\times 2\times 2\times 2\times 5\times 5$

$=3^2\times 2^4\times 5^2$.

We know, a perfect cube has multiples of 3 as powers of factors,

i.e. here, the number has to be multiplied by $3\times 2^2\times 5=60$ to make it a perfect cube.

Therefore, the new number $=3600\times 60=216000$.

Then, $\sqrt[3]{3216000}$ $=\sqrt[3]{33^3\times 2^6\times 5^3}$

$=3\times 2^2\times 5=60$.