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Multiply 210125 by the smallest number so that the product is a perfect cube. Also, find out the cube root of the product.
We have to find the smallest number by which 210125 must be multiplied so that the product is a perfect cube and find the cube root of the product.
Prime factorisation of 210125 is,
Grouping the factors in triplets of equal factors, we see that $41^2$ is left.
In order to make 210125 a perfect cube, we have to multiply it by $41$.
The smallest number by which 210125 must be multiplied so that the product is a perfect cube is 41 and the cube root of the product is 205.
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