How do you divide a square into 3 equal squares of the same size?

Cube root it.

the square of a cubed number can be divided into 3 equal squares

(Ae3)e2 = Ae(3x2) or Ae6

this is also equal to (Ae2)E3

as long as a number can be expresses as a root number with an exponent equal to 6 the cube root of that number is a square of the root

Example: 64 can be divided into 8 x 8 or 4 x 4 x 4

64 is the square of 8 and the cube of 4

4 is the square of 2, 8 is the cube of 2

per the above formula:

(2e3)e2 = 2e6 = (2e2)e3

= 8e2 and 4e3

more simply:

2 x 2 x 2 x 2 x 2 x 2 = 64

8 x 8 = 64 (64 is a square)

4 x 4 x 4 = 64 (64 is also a cube)

2 x 2 = 4 (4 is a square)