Question

Can the cube root of a two-digit number be a 3-digit number? Support
your answer with proper examples

Answer 1

The examples :

Cubes between 1 and 100 that are two digit are as follows :

27

64

These are the only two digit number perfect cubes we have.

Their cube roots are as follows :

∛27 = 3

∛64 = 4

From the cube roots above, we see that the cube root of a two digit number gives a one digit number.

The answer is thus no.

Answer 2

The answer is obviously no. But the way we prove it matters.

So, finding a cube-root of any number, not only a two digit number will be definitely less than the original number. So, there's no point of getting a three digit number from cube-root of a 2 digit number.

Now lets prove this mathematically.

The smallest two digit perfect cube is 27 and largest two digit perfect cube is 64.

The cuberoot of both these numbers are 3 and 4 which is one digit.

I hope you're clear with the answer by now.