Question

By what smallest number should 19652 be multiplied so that the product becomes a perfect cube. Also, find the cube root of the product.

Answer 1

Answer:

We have,

19652=2×2×17×17×17

After grouping the prime factors in triplets, it’s seen that factors 2×2 are left ungrouped in 3’s.

19652=2×2×(17×17×17)

So, in order to complete it in a triplet one more 2 is needed.

Thus, the smallest number which should be multiplied to 19652 in order to make it a perfect cube is 2.