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Pascal's Triangle

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  • jule143@aol.com
    I have read that one can extract square roots utilizing Pascal s Triangle. Is anyone aware of the technique ?
    Message 1 of 2 , Apr 4 10:38 AM
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      I have read that one can extract square roots utilizing Pascal's Triangle.
      Is anyone aware of the technique ?
    • David Hobby
      Message 2 of 2 , Apr 9 8:20 PM
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        >
        > I have read that one can extract square roots utilizing Pascal's Triangle.
        > Is anyone aware of the technique ?
        >
        Though it's not really on-topic for our list, I was hoping someone
        knew a method... I was curious.
        So here's the one I made up, feel free to better it.

        One has a LARGE Pascal's triangle at hand, I take it? All I need is
        the edge of it, though:
        1
        1
        2 1
        3 1
        6 4 1
        10 5 1
        15 6 1
        21 7 1
        28 8 1
        36 9 1
        and so on...

        I look at the 6,10,15,21,28,36,... diagonal, and pick the entry
        closest to half of the number I want the square root of. So if I want
        the square root of 70, I'll go with the 36. Then an approximation to the
        square root is the average of the two numbers next to it in the next
        diagonal over, (8 + 9)/2 = 8.5 . You want more accuracy? Simply multiply
        your number by 100 (or 10,000 or 1,000,000 or ...). So to approximate
        the square root of 7000, one looks for 3500, and finds:

        1
        1
        82 1
        83 1
        3486 84 1

        this gives 7000^.5 approximately equal to 83.5, and so
        70^.5 is approximately equal to 8.35 ...
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