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guys, just out of curiosity, how often do you guys tend to memorize the squares and cubes? what's the recommended length of your memorization in order to work around such numbers as smoothly as possibe? for example, do you memorize the squares from 1 all the way to 20? 30? 40? plus, i'd also like to get your input with memorizing the 'powers' such as 2^1 all the way to 2^10? or is it more? and what about the 3's or 4's? i'd really like to know what's the recommended level of memorization here.

I agree with bmw. Athough to memorize cubes till 10 is a bit too much for me.

I use a trick, if you can call it that way, which I find particularly helpful.

If you want to calculate something like 19^2, you can think as follows:

19*19 = (20-1)*(20-1) = (20-1)^2 = 400-40+1 = 361

Same holds if you want to calculate products like 23*23. To transform in into (20+3)^2 = 400+120+9=529 works in less than 10 secs, especially if you are good in numbers.

Last but not least, there is another trick I use which is extremely helpful.

If you encounter products in the form 999*1001, or 19*21, use (a+b)(a-b)

guys, just out of curiosity, how often do you guys tend to memorize the squares and cubes? what's the recommended length of your memorization in order to work around such numbers as smoothly as possibe? for example, do you memorize the squares from 1 all the way to 20? 30? 40? plus, i'd also like to get your input with memorizing the 'powers' such as 2^1 all the way to 2^10? or is it more? and what about the 3's or 4's? i'd really like to know what's the recommended level of memorization here.

thanks

i memorized all squares to 20 and all cubes till 10. anything else is a burden on my brain and useless info that can be figured out on paper.

also memorized the first 5 overlaps of cubes and squares.

ok then, well it is an excellent strategy when you're multiplying, but when you have to go backwards, such as finding the square root or cube root, then that's when you will get into the risk of wasting time. I had a gmat teacher from the columbia business school, who suggested memoring the squares all the way to 32 and the cubes all the way to 20. i think that will help us computing our numbers much faster. just thought to share this with you guys.

bmwhype2, what are those rules? lets make this thread full of tricks, memorizing tips, and etc. i'm sure this can be a really interesting one!

something else that i would like to add. also memorize the square roots of 5 to 10.

those can be helpful when dealing with a problem that would make use subtract such numbers from another. i'm assuming that you guys already know your square roots from 1 to 4...heheheh....