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Math Help - A fast little trick for mental calculation of x^2

  1. #1
    dud
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    A fast little trick for mental calculation of x^2

    I suppose many might have figured this out, but it's a neat little mind trick for calculating the product of a number between 10 - 19 with itself. I stumbled upon it as I was riding the bus back home from my math class, and thought it might come in handy for those who don't know it yet!

    Multiplication:
    <br />
13^2 = 169<br />
    Think:
    <br />
1^2 = 1<br />
    <br />
3+3 = 6<br />
    <br />
3^2 = 9<br />
    Excellent, should take a normally gifted person about \phi seconds!

    For numbers which gives two digits for any of the operations, you do the same basically. But just remember that you need to summarize the results you get correctly.
    Multiplication:
    <br />
17^2 = 289<br />
    Think:
    <br />
1^2 = 1<br />
    <br />
7+7 = 14<br />
    <br />
7^2 = 49<br />
    If you remember the addition you need to do, it shouldn't take much longer.

    This metod works excellently for myself, and it will usually take me between 2-5 seconds to calculate the product of any number between 10-19 multiplicated with itself.

    A bit more mathematically we can write:
    <br />
f(x) = x^2 \Leftrightarrow 100\alpha^2 + 20\beta + \beta^2, x \epsilon [10, 19]<br />
    Where alpha denotes the first digit of the product, and beta the second.
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  2. #2
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    Quote Originally Posted by dud
    I suppose many might have figured this out, but it's a neat little trick...
    Hey,

    how about this little trick:

    37 \cdot 43 = 1600 - 9
    or 79 \cdot 81 = 6400 - 1

    For heaven's sake, why that? Can you explain how it works?

    Have some fun!

    Bye
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  3. #3
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    Quote Originally Posted by dud
    I suppose many might have figured this out, but it's a neat little trick...
    Hey,

    here I'm again. The following way to calculate a product of two numbers is really tricky to explain - but try it:

    \begin{array}{l cr} 37 \cdot &42\\ 18 & 84\\9 & 168\\4&336\\2&672\\1&1344\end{array}

    You've to delete now all numbers of the second column corresponding to an even number in the first column.
    That leaves yo with: 42+168+1344

    and the result of this sum is 1554 = 37 * 42

    Now it's your turn.

    Have much fun!

    Bye
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  4. #4
    dud
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    That last one is neat, but it might happen to be a little too much to keep in your head at one time! Especially if you're attention is diverted for a bit.
    Also I recon it would take a few minutes of effort for most numbers, right?

    But a good little thing indeed.
    Mine is cooler though!
    Has anyone used/seen this one before by the way?
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