Results 1 to 4 of 4

Thread: A fast little trick for mental calculation of x^2

  1. #1
    dud
    dud is offline
    Newbie
    Joined
    Jan 2006
    From
    Trondheim, Norway
    Posts
    20

    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:
    $\displaystyle
    13^2 = 169
    $
    Think:
    $\displaystyle
    1^2 = 1
    $
    $\displaystyle
    3+3 = 6
    $
    $\displaystyle
    3^2 = 9
    $
    Excellent, should take a normally gifted person about $\displaystyle \phi$ 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:
    $\displaystyle
    17^2 = 289
    $
    Think:
    $\displaystyle
    1^2 = 1
    $
    $\displaystyle
    7+7 = 14
    $
    $\displaystyle
    7^2 = 49
    $
    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:
    $\displaystyle
    f(x) = x^2 \Leftrightarrow 100\alpha^2 + 20\beta + \beta^2, x \epsilon [10, 19]
    $
    Where alpha denotes the first digit of the product, and beta the second.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,854
    Thanks
    138
    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:

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

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

    Have some fun!

    Bye
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,854
    Thanks
    138
    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:

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

    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
    Follow Math Help Forum on Facebook and Google+

  4. #4
    dud
    dud is offline
    Newbie
    Joined
    Jan 2006
    From
    Trondheim, Norway
    Posts
    20
    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?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Mental calculation
    Posted in the Math Puzzles Forum
    Replies: 3
    Last Post: Oct 7th 2009, 08:01 AM
  2. Mental Blockage
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Apr 25th 2009, 03:58 PM
  3. Mental math program
    Posted in the Math Software Forum
    Replies: 1
    Last Post: Mar 7th 2008, 11:55 AM
  4. [SOLVED] Mental math
    Posted in the Math Forum
    Replies: 2
    Last Post: Sep 30th 2007, 06:57 AM

Search Tags


/mathhelpforum @mathhelpforum