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Mathcast #4: Quick squaring of 2-digit numbers

Here's a video on how to quickly square a 2-digit number. The technique is based on this algebra:

If you have a number with digits "ab" then the number is 10a+b.
(10a+b)^2 = 100a^2+20ab+b^2.

If you enjoy this video check out all of the Wild About Math! mathcasts.

Comments (10) Trackbacks (1)
  1. So you’ve hooked me. In this case, your method is fine, but I still prefer a^2 = (a+b)(a-b) + b^2.

    67 squared? (64)(70) + 9

    The best of all would be to have full command of multiple techniques.


  2. Jonathan,

    I agree completely that having full command of multiple techniques is best. For me that’s always been the fun thing about arithmetic, finding the pattern among the numbers and deciding in the moment which technique I was going to apply.

  3. If I watch too many more of these videos Sol, there’s a real danger I might start really getting interested in math.

  4. Karen,

    Scary thought, isn’t it! These things happen.

  5. Wow, very cool. My brain didn’t kick in for math until college and now I am rusty. Wondered what you were doing over here and looks cool!

  6. I think that your “trick” regarding squaring is far too complicated…
    For example…43 Sqared…

    First ask yourself…how far from 50?, Easy..you get 7, now subtract that from 25 and you get
    18..which is the first part of your answer…

    Then simply square what you added to 25..and you get 49…which is the second part of your answer… 1849

    Try another?

    62 squared?

    In this case it is over 50 and 12 from 50…so instead of subtracting…I ADD…12 to 25..get
    37…then squaring 12, we get 144..

    Simply add the 1 to 37, and we get 3844

    Isn’t this easier than your method?

    Thank you

  7. Jt,

    What you’re demonstrating is a Vedic technique for rapid multiplication. I’ve been thinking of making a video to show the use of bases in the Vedic approach. You’ve inspired me to go ahead and do that.

  8. I found an easier way to square 50′s.
    57 squared. (57 x 57) Think of 50 as 25, add 7 to 25 and you have 32. Square 7, and you have 49. So you answer is 3249.

    For 62 squared, think of 60 as 36. Add 2 to 36 and you have 38, double to second number, and than square the orginal number. This it the mental application: 62×62 is 36 + 2 = 38 (first part of answer)Double the two = 4, square the 2 = 4 again. So the answer is 3844.

    For 43 x 43 think of the 40 as 15, 15 + 3 = 18. 43 is 7 from 50 so, 7 squared is 49. The answer 1849.

  9. How do you determine the values of a & b?

  10. How is that easier? One still has to multiply a two 2 digit numbers in one’s head. You might as well just multiply the original number to be squared.

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