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A interesting way to square 4 digit numbers

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  • webcash56
    Hello, everyone: Example of a squaring method: To square 3915: Square 39= 1521 Square 15= 225 Separate them in groups of 2 digits: 15 21 2 25 Now merge them:
    Message 1 of 4 , Oct 1 9:34 PM
      Hello, everyone:

      Example of a squaring method:

      To square 3915:

      Square 39= 1521

      Square 15= 225

      Separate them in groups of 2 digits:

      15 21 2 25

      Now merge them:

      15 21+2 25
      15 23 25

      More merging:

      15 15+23 23+25 25

      15 38 48 25

      Now with the original number:

      3915
      39 15
      Absolute difference=39-15=24

      Square 24=576

      Now subtract this way:

      15 38 48 25
      - 5 76 00
      --------------
      15 32 72 25

      Answer:15,327,225

      I hope that I have made this clear enough.
      Note: the 2 digit squares are very easy, knowing them all.

      Wonder if anyone else uses it.

      -Steven W.
    • rondrond1
      Hi Steven, This is an interesting variation on a method I wrote up before for general 4x4-digit multiplication. See
      Message 2 of 4 , Oct 2 10:03 AM
        Hi Steven,

        This is an interesting variation on a method I wrote up before for general 4x4-digit multiplication. See

        http://www.myreckonings.com/Dead_Reckoning/Chapter_2/Materials/A%20Method%20for%204x4%20Digit%20Mental%20Multiplications.pdf

        I like how you did the second merge right after the first merge, though. In my case I include those values into the final merge at the end, but waiting like that means more numbers to handle at that time. I'll have to practice merging earlier and see if that's easier for me.

        Thanks,

        Ron Doerfler

        P.S. You may be interested in seeing (and improving) other papers on mental calculation on my website:

        http://www.myreckonings.com/Dead_Reckoning/Online/Online_Material.htm



        --- In MentalCalculation@yahoogroups.com, "webcash56" <webcash56@...> wrote:
        >
        > Hello, everyone:
        >
        > Example of a squaring method:
        >
        > To square 3915:
        >
        > Square 39= 1521
        >
        > Square 15= 225
        >
        > Separate them in groups of 2 digits:
        >
        > 15 21 2 25
        >
        > Now merge them:
        >
        > 15 21+2 25
        > 15 23 25
        >
        > More merging:
        >
        > 15 15+23 23+25 25
        >
        > 15 38 48 25
        >
        > Now with the original number:
        >
        > 3915
        > 39 15
        > Absolute difference=39-15=24
        >
        > Square 24=576
        >
        > Now subtract this way:
        >
        > 15 38 48 25
        > - 5 76 00
        > --------------
        > 15 32 72 25
        >
        > Answer:15,327,225
        >
        > I hope that I have made this clear enough.
        > Note: the 2 digit squares are very easy, knowing them all.
        >
        > Wonder if anyone else uses it.
        >
        > -Steven W.
        >
      • webcash56
        Hi Ron, Thanks! It is based on your method, with a few optimizations of my own. Also, I enjoy your book! -Steven W.
        Message 3 of 4 , Oct 2 4:20 PM
          Hi Ron,

          Thanks! It is based on your method, with a few optimizations of my own. Also, I enjoy your book!

          -Steven W.

          --- In MentalCalculation@yahoogroups.com, "rondrond1" <pub@...> wrote:
          >
          > Hi Steven,
          >
          > This is an interesting variation on a method I wrote up before for general 4x4-digit multiplication. See
          >
          > http://www.myreckonings.com/Dead_Reckoning/Chapter_2/Materials/A%20Method%20for%204x4%20Digit%20Mental%20Multiplications.pdf
          >
          > I like how you did the second merge right after the first merge, though. In my case I include those values into the final merge at the end, but waiting like that means more numbers to handle at that time. I'll have to practice merging earlier and see if that's easier for me.
          >
          > Thanks,
          >
          > Ron Doerfler
          >
          > P.S. You may be interested in seeing (and improving) other papers on mental calculation on my website:
          >
          > http://www.myreckonings.com/Dead_Reckoning/Online/Online_Material.htm
          >
          >
          >
          > --- In MentalCalculation@yahoogroups.com, "webcash56" <webcash56@> wrote:
          > >
          > > Hello, everyone:
          > >
          > > Example of a squaring method:
          > >
          > > To square 3915:
          > >
          > > Square 39= 1521
          > >
          > > Square 15= 225
          > >
          > > Separate them in groups of 2 digits:
          > >
          > > 15 21 2 25
          > >
          > > Now merge them:
          > >
          > > 15 21+2 25
          > > 15 23 25
          > >
          > > More merging:
          > >
          > > 15 15+23 23+25 25
          > >
          > > 15 38 48 25
          > >
          > > Now with the original number:
          > >
          > > 3915
          > > 39 15
          > > Absolute difference=39-15=24
          > >
          > > Square 24=576
          > >
          > > Now subtract this way:
          > >
          > > 15 38 48 25
          > > - 5 76 00
          > > --------------
          > > 15 32 72 25
          > >
          > > Answer:15,327,225
          > >
          > > I hope that I have made this clear enough.
          > > Note: the 2 digit squares are very easy, knowing them all.
          > >
          > > Wonder if anyone else uses it.
          > >
          > > -Steven W.
          > >
          >
        • rondrond1
          Hi Steven, Thanks for the nice words, and thanks to Mr. Bouman for recommending my book in this group the other day. Mr. Bouman and I have exchanged emails
          Message 4 of 4 , Oct 2 6:28 PM
            Hi Steven,

            Thanks for the nice words, and thanks to Mr. Bouman for recommending my book in this group the other day. Mr. Bouman and I have exchanged emails lately, and he is just as pleasant one-on-one as he is here in this group.

            I always recommend to people who get my book that they download the the errata and additional notes for the book at:

            http://www.myreckonings.com/Dead_Reckoning/Latest%20Notes%20and%20Errata.pdf

            There are some typos and mistakes in the book, nothing major in the way of the methods themselves but important nonetheless. Most of these are typos in the text or intermediate steps, but there is at least one case where the final formula has a sign reversed. The book was published without my corrections from the galley proofs, and while I have inquired over the years about a writing a new edition I have not been successful with the publisher yet. Meanwhile you may want to mark up your copy.

            Regards,

            Ron

            --- In MentalCalculation@yahoogroups.com, "webcash56" <webcash56@...> wrote:
            >
            > Hi Ron,
            >
            > Thanks! It is based on your method, with a few optimizations of my own. Also, I enjoy your book!
            >
            > -Steven W.
            >
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