Question

125 is.a perfect square or perfect cube

Answer 1

It is a perfect cube with sides of 5.

Explanation:

If 125 was a perfect square, there would be a whole number A which, squared, would give us 125.

`A^2 = 125\\A = \pm 11.18...`

We can see that the roots are not whole numbers.

(Tip: without a calculator, we can find this by testing
`10^2 \ 11^2\ 12^2` to see if any give us 125. We get 100, 121, 144 respectively. None of them is 125.)

If it was a perfect cube, there would be a whole number B which, cubed, would give us 125.

`B^3 = 125\\B = \sqrt[3]{125} \\B = 5`

As we can see, there IS a whole number B: 5 !

(Without a calculator, like the previous one, we could try
`4^3\ 5^3\ 6^3` and we'd find that
`5^3` = 125)

Answer: It is a perfect cube with sides of 5.

Answer 2

Perfect cube

Explanation:

5 x 5 x5 = 125

5x5= 25

25x5 =125