Memorizing squares up to 999?

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#1 24 September, 2017 - 15:49
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Memorizing squares up to 999?


Several times while perusing the forums I’ve seen referencing to people memorizing squares up to 999. I’ve recently finished memorizing all squares up to 99, and I’ve noticed that I seem to memorize numbers rather easily, so I was thinking about just starting to memorize squares up to 999, learning one each day. Before I started, though, I was just curious about the advantages. Does it make sense to invest the time to do this? Would my time be better spent on something else?

I made a short list of advantages that I came up with (in addition to the obvious one: you don’t have to calculate 3-digit squares):
1.) You can immediately recognize all perfect squares up to 6 digits.

2.) You can immediately approximate a square root that has up to 6 digits by interpolating between known squares.

3.) You can quickly calculate 4-digit squares using the difference of squares (a^2 = (a + b)(a - b) + b^2, where b is a 3-digit number).

4.) Reduce the time required to calculate 3x3’s where the numbers are close to the same value (ex: 337 x 335 = 335^2 + 2*335) or where the terms can be factored to produce a square (ex: 337 x 674 = 2*(337^2)).

Is there any advantage that I missed?

25 September, 2017 - 21:49
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Joined: 4 months 2 weeks ago

The more I think about it, the more I like this idea. I think I'll also use this opportunity to create images and words for each number, that way I accomplish two things simultaneously. For instance, I'll memorize 303^2 = 91,809, and I'll use the word museum to represent the number 303, visualizing the inside of a museum with all its paintings. I was also thinking about using a color system to identify prime numbers. Any object used to represent a prime number will be red with a red background.

Learning one a day, this will take me two and a half years. That's not too bad.

26 September, 2017 - 01:06
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Joined: 5 years 10 months ago

A disadvantage IMHO is that it kills creativity.
For example you would modify the calculation below as:

RubiksKid wrote:

337 x 335 = 335^2 + 2*335

Of course that works and is a great way of finding the solution!
However; you might have overseen that possibly quicker is:

337 x 335 = 336^2 - 1

(Or:
337 x 335 = 330 X 342 + 5*7
Or:
337 x 335 = 300 X 372 + 36^2)

That is why I always advise to work on finding solutions in multiple ways.
Always ask your brain 'can I find a different way of solving this?'.
Then do the calculation in each and every way you can find.

Apart from that it is a great endeavour and I applaud you for doing it!

26 September, 2017 - 11:44
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Joined: 4 months 2 weeks ago

You make a good point. I think I'll just make it a habit to explore alternate solution paths while practicing.

26 September, 2017 - 17:07
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Joined: 5 months 3 weeks ago

Hi RubiksKid and everybody!,

I have thinked exactly in this possibility and I conclude that is a wasted time because is posible to calculate super fast.

Did you see Arthur Benjamin? in many videos you can see him squaring 3 digit numbers, for example here:

https://www.youtube.com/watch?v=a1mNqa7OZ_o

Arthur reconize that 2 digit squares is automatic for him, but 3 digit squares he does the calculation, he only knows a few by memory.

Knowing 2 digit numbers square is an advantage for to squaring a 3 digit number fast. That's the advantage that Arthur uses apart from the fact that he knows multiplication table to 100 (example: 45 x 7).

Knowing the multiplication table to 100 like 37 x 3 is in my opinion basically the only really usefull thing to memorize in calculation, is very very usefull, is used in squares, multiplications, divisions...
In fact knowing multilication table to 100 very fast involves a great deal of time.

About calculating 3 digit square the great advantage is that if you calculate them alot you probably can memorize all them after alot of calculation. But that process of memorization IS NOT WASTED TIME because you PRACTICE CALCULATION.

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NOTE: SORRY IF MY ENGLISH HAVE ERRORS, IF I SPEAK IN SPANISH, THE MAJORITY OF PEOPLE CAN'T UNDERSTAND ME. I'M IN THE PROCESS OF LEARN ENGLISH.

27 September, 2017 - 12:05
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Joined: 4 months 2 weeks ago

Thanks for your input, Adrian. You do make a good point. And actually I've decided to hold off on memorizing the squares for now and instead devote my time to learning a word/sound pair for each number up to 999. This is because I think the utility of having a pre-associated word for each number is far greater than knowing all my squares. Plus I can do it a lot faster. I'll come back to squares later.

And I like your comment regarding learning all 2x1's. I actually have flashcards for all of them in a stack by my bed. I look at them for a few minutes each night before going to bed. I thought that eventually I'd memorize them passively.

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