Question

What is the smallest whole number that can be multiplied by 300 such that the product is a perfect cube?

Answer 1

The smallest whole number that can be multiplied by 300 so that the product is a perfect cube is 12 (I think)

Answer 2

300=2×2×5×5×3

We observe that 2 and 5 are grouped in pairs and the 3 is left unpaired.

If we multiply 300 by the factor 3 then  

300×3=2×2×5×5×3×3

900=2×2×5×5×3×3 which is a perfect square.

∴ Required number is 3

root of 900  =30