First, I cut the grid into four pieces along these lines.
Then, I separate the pieces like this.
Now, I rearrange the pieces like this.
And join them back together to form a square.
That leaves us with a grid containing 64 identical squares.
(Do the math: 8 x 8 = 64.)
The 65th square has vanished before your very eyes!
Did anyone ever tell you that you have very eyes?
Here it is!