We had to memorize the squares up to 21 in grade school. The book is absolutely right though -- memorizing squares/cubes/2^n is a math superpower. It's extreme

We had to memorize the squares up to 21 in grade school. The book is absolutely right though -- memorizing squares/cubes/2^n is a math superpower. It's extremely useful when solving textbook problems or when just exploring math on your own. I've seen the powers of 3 so often they've immediately become recognizable, 27,81,243, just as I'm sure most people immediately recognize 81 as a square when they see it -- it just "pops out" from the page. This holds for simple identities too. Having things like x^2 - y^2 = (x+y)(x-y) immediately come to mind when you see just one half of the identity is ridiculously useful.