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Thread: calculate root

  1. #1
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    calculate root

    How the calculator calculate the root of number, e.g. sqrt-2?
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  2. #2
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  3. #3
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    Re: calculate root

    O.K.
    I have my source and I will quote a part from it in my words. O.K?
    There are some ways from to calculate root.
    One of the way is Taylor Polynomial.
    If a function f is very "nice" so can approximate its values by polynomial.
    Examples of that "nice" function are: roots, sinus, cosines and another kinds of it.
    What the property of the this "nice" function? It can be derived infinitely times.

    How I should know if function is derived any time (and example/website, if possible, one can bring on how can it combined by calculating root of two by calculator)?
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  4. #4
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    Re: calculate root

    While using the Taylor polynomial to approximate a given function is very basic, the "CORDIC" method is now more commonly used:https://en.wikipedia.org/wiki/Method...e_roots#CORDIC
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  5. #5
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    Re: calculate root

    O.K.
    So why this method works?
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  6. #6
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    Re: calculate root

    I always use either the Babylonian method, for its simplicity or the approximation
    $$\sqrt{a} \approx n + \frac{a-n^2}{2n} \qquad n = \lfloor \sqrt{a} \rfloor, \, \text{the greatest integer whose square does not exceed $a$}$$
    when accuracy is not so important as speed.

    The approximation
    $$\sqrt{a} \approx n - \frac{n^2-a}{2n} \qquad n = \lceil \sqrt{a} \rceil, \, \text{the least integer whose square is not smaller than $a$}$$
    is similar to the above.
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  7. #7
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    Re: calculate root

    Using the binomial theorem, and for appropriate $\displaystyle \ a \ \ and \ \ b, $
    $\displaystyle \sqrt{a^2 + b} \ \approx \ a \ + \ \dfrac{b}{2a}$

    If $\displaystyle \ a_1 \ = \ 1.4, \ \ then \ \ b \ = \ 0.04, \ \ and \ \ a_2 \ \approx \ 1.414285714$
    Last edited by greg1313; Dec 28th 2018 at 11:06 PM.
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