what are two numbers between 1 and 100 that are perfect square numbers and perfect cubed numbers??¿?

Technically you can tell your teacher there is only one number, it's 64. You can't count 1 because it's not BETWEEN 1 & 100, so I would turn in the answers as 1 & 64 so the teacher knows you understood the principle but add this as a note.

64 :

8 x 8 = 64

4 x 4 x 4 = 64

and 1

1 x 1 x 1 = 1

1 x 1 = 1

The two are 1 and 64.

Since 1^2 = 1 and 1^3 = 1

now 8^2 = 64 and 4^3 = 64

If you like 8 can be written as 4x2 so 8^2 = (4x2)^2 = 4^2 x 2^2 = 4^2 x 4 = 4^3

1 and 64 obtained by observing the squares and cubes of numbers 1 through 4...can't use 5 or more because their cube is more than 100.

so 1 squared equals 1 and 1 cubed equals 1

2 squared is 4 and cubed is 8, but 4 is not a perfect cube and 8 is not a perfect square

3 squared is 9 and cubed is 27, but 9 is not a perfect cube and 27 is not a perfect square

4 squared is 16 and cubed is 64. 16 is not a perfect cube, but 64 is a perfect square (8 squared)

1 and 64

Hi Bekka,

Start at 1, and start squaring numbers until you get to, or go past, 100:

Square numbers in range:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Again, start at one, this time, cube the numbers. Stop when you get to, or go past, 100:

Cube numbers in range:

1, 8, 27, 64.

The only numbers on both lists are:

1 and 64.

list all the cubes: 1, 8, 27, 64. the only two are 1 and 64

64-> 4•4•4, 8•8

1-> 1•1•1, 1•1