This is by trial and error. By chance only. Hit or miss. Yes, even a 5th grader can solve this puzzle. I don't know how logic is used here. It's more of doodling, or "drawing-drawing", than "2+2"or reasoning.
There could be some other ways but here is one way that I found by doodling.
I sketched 3 squares. One 6x6, one 8x8, and one 10x10. Done oblique or skewed cuttings, used the 6-8-10 right triangle, etc. Finally I stumbled onto a correct way of doing it. I doodled it on the 10x10 square.
I subdivided all the 3 squares into stacks or mosaics of 2x2 squares. So the 6x6 has nine 2x2's, the 8x8 has sixteen 2x2's, the 10x10 has twenty five 2x2's.
[6x6 reads "six by six". 2x2 is "two by two". Etc.]
The 6x6 square:
At its upper lefthand corner, cut away a 4x4 square
Then place this 4x4 piece on top of the other piece, which is an "L" facing to the left, whose equal legs are three 2x2's each. [How hard it is to explain. If I could only draw on this board....]
Now the resulting figure is the left side of the 10x10 square. Its height is five 2x2's. Its top is a row of two 2x2's. Its bottom or base is a row of three 2x2's. [If you could understand or follow so far, congratulations.]
The 8x8 square:
At its upper righthand corner, cut away a column (vertical) of two 2x2's.
Then place the other (bigger) piece snugly, like jigsaw puzzle, to the existing or earlier-formed figure.
Then place the smaller piece of two 2x2's horizontally below the bottom of the said bigger piece.
Voila! You have your 10x10 square.
[If you are still reading this, and you understood what I just described, gimme your five, Up Here!]