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Find the smallest number which when multiplied with 3600 will make the product a perfect cube. Further, find the cube root of the product.
We have to find the smallest number by which 3600 must be multiplied so that the product is a perfect cube and find the cube root of the product.
Prime factorisation of 3600 is,
Grouping the factors in triplets of equal factors, we see that $2, 3^2$ and $5^2$ are left.
In order to make 3600 a perfect cube, we have to multiply it by $2^2\times3\times5=60$.
The smallest number by which 3600 must be multiplied so that the product is a perfect cube is 60 and the cube root of the product is 60.
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