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Math Help - Manual calculation of square roots

  1. #1
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    Manual calculation of square roots

    Years ago I was taught how to calculate the exact square root of any number manually(no calculator).Now I just dont remember anything.
    By the same analogy,how do you find the square root of a prime integer?
    Thank you guys.
    Tbone
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  2. #2
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    Quote Originally Posted by tbone1209 View Post
    Years ago I was taught how to calculate the exact square root of any number manually(no calculator).Now I just dont remember anything.
    By the same analogy,how do you find the square root of a prime integer?
    Thank you guys.
    Tbone
    Are you asking "How do you get the decimal approximation for the square root of a prime integer?"
    Because you can't evaluate the square root of a prime integer exactly...

    Babylonian
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  3. #3
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    Nor can you evaluate the square root of any integer which is not the square of another integer.

    It has been proved that if n cannot be written n = c^2 with c \in N, then \sqrt{n} is irrationnal (cannot be finitely written using decimals)

    Little bonus : since p is prime, it cannot be written p = c^2 with c \in N (that would mean that p is composite and not prime), thus \sqrt{p} is irrationnal.

    Now you can approximate : take \sqrt{7}, for example.
    You know that 4 < 7 < 9, thus \sqrt{4} < \sqrt{7} < \sqrt{9}
    So 2 < \sqrt{7} < 3

    Rince, reiterate (with closer bounds), and after some time you will get a pretty good approximation.
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  4. #4
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    Thanks guys!
    Its nice to know.
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  5. #5
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    I think this may be what you have in mind.

    Math Forum - Ask Dr. Math

    It's how I was taught to do it, back in the Dark Ages (pre-calculator).
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  6. #6
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    Back in the Dark Ages (pre-calculator).

    That's exactly what I am looking for, Dr.Awkward.
    "Dark Ages" I like that.I was at that critical period before;somehow thru the years I just could not recall that technique a 100%.I was just trying to show my kid in math that this could be done.Thanks again Dr.

    I am a very new newbie with this forum.I read and gone through a lot of threads until I found this thread regarding this square root thing;not exactly what I was looking for and thats why my question was posted, with the same thread,for some help.There was no intention to break the rules for not starting a new thread and got a warning for it.I will remember now!

    Above all,all you guys are great!I really appreciate the prompt response either way and thank you, Dr.Awkward.

    Merry Christmas to you all

    Tbone
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