Question

125 is.a perfect square or perfect cube

Answer 1

Answer:

It is a perfect cube with sides of 5.

Step-by-step 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

Answer:

Perfect cube

Step-by-step explanation:

5 x 5 x5 = 125

5x5= 25

25x5 =125