Question

is 5400 a perfect cube? if not, find the smallest natural number by which 5400 must be divided so that the quotient would be a perfect cube​

Answer 1

Answer:

when we look at the number, it is not a perfect cube. But when we divide 25 of it, get a perfect cube.

Let’s see how is it….

5400 = 2 x 2 x 2 x 5 x 5 x 3 x 3 x 3.

Here, we can clearly see that there are 3 two(s) and three(s) inside 5400.However, there are 2 five(s) inside 5400 too. So, when we perform the cube root, the 3 two(s) and 3 three(s) shall yield one 2 and one 3, but 5 being 2 in number cannot yield a perfect cube. Thus on dividing (removing) the 5 x 5 part off the expansion of 5400, we can get a perfect cube that is 216.