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# memorizing squares, cubes, etc.

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SVP
Joined: 21 Jul 2006
Posts: 1551
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memorizing squares, cubes, etc. [#permalink]  27 Nov 2007, 04:28
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
Manager
Joined: 10 Aug 2007
Posts: 63
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2
KUDOS
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.
CEO
Joined: 21 Jan 2007
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Location: New York City
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Kudos [?]: 350 [0], given: 4

Re: memorizing squares, cubes, etc. [#permalink]  27 Nov 2007, 04:51
tarek99 wrote:
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.
SVP
Joined: 21 Jul 2006
Posts: 1551
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Kudos [?]: 305 [0], given: 1

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.
Senior Manager
Joined: 09 Oct 2007
Posts: 467
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Kudos [?]: 22 [0], given: 1

The more we memorize the better, I guess. That should give us some extra valuable seconds.

I've also memorized 8!, 7!... 3! so that I don't have to think to about it.

I've memorized the primes from 2-47, do I need more?

I 've been wondering about this too. What other stuff should we memorize? Bring it on. There's alway more stuff I can memorize on my way to work...

Good luck all.
SVP
Joined: 21 Jul 2006
Posts: 1551
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Kudos [?]: 305 [0], given: 1

for primes, i would memorize from 2 all the way to 113. i'll list them down for you:

2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
67
71
73
79
83
89
97
101
103
107
109
113

CEO
Joined: 21 Jan 2007
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Location: New York City
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Kudos [?]: 350 [0], given: 4

one of the oddball things i memorized was the 2 divisibility rules of 7, because one of the challenge questions asked about it.
SVP
Joined: 21 Jul 2006
Posts: 1551
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Kudos [?]: 305 [0], given: 1

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....
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