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27 Nov 2007, 05:28
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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.
thanks
thanks
27 Nov 2007, 07:44
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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)
19*21 = (20-1)*(20+1) = 20^2-1 = 399
999*1001 = (1000-1)*(1000+1) = 10^6 -1 = 999999
Hope this helps.
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)
19*21 = (20-1)*(20+1) = 20^2-1 = 399
999*1001 = (1000-1)*(1000+1) = 10^6 -1 = 999999
Hope this helps.
General Discussion
27 Nov 2007, 05:51
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tarek99
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.
