

How to square numbers closer to 50 in less than 5 seconds - mquaes
http://mathema-tricks.blogspot.com/2012/03/squaring-numbers-from-30-70.html

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dalke
I am getting really sick of these "mathema-tricks" postings, all from the same
author, whose 50+ posts are all to do with the same web site.

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drostie
The tl;dr: (50 + x)² = (25 + x) * 100 + x². If you know the squares from 0 to
25 you can then bootstrap the squares to 75. At the very least, between 41 and
59 you don't have to deal with carrying and can just say 42² = (25 - 8) 100 +
8² = 1764.

I would add that (100 + x)² = (100 + 2x) 100 + x², and doubling is efficient,
too. So 92² = (100 - 16) 100 + 8² = 8464.

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swah
I'd do that kind of math as: 53ˆ2 = 50x50 + 3x50 + 3x50 + 3x3. No "trick" to
remember (well perhaps that 50 _50 is like 5_ 5 plus that many zeroes at the
end of the result)

