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Cubic Root

  1. Oct 29, 2007 #1
    I still remember how to extract a square root without a computer but could somebody remind me the technique to find a cubic root just with the pencil and paper?
    Last edited: Oct 29, 2007
  2. jcsd
  3. Oct 29, 2007 #2


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    I would suggest using some Newton-Raphson scheme.

    1. Let [tex]f(x)=x^{3}-a[/tex]
    You are to find X so that f(X)=0.

    2. Pick an initial value [tex]x_{0}\to{f}(x_{0})=x_{0}^{3}-a[/tex]

    3. The equation for the tangent line L(x)=at [tex](x_{0},f(x_{0})[/tex] is given by:

    4- Let the next iteration point be the x-intercept of L(x):

    5. Or, in this case, the iterative scheme becomes:
    That is:
    [tex]x_{n}=\frac{2x_{n-1}^{3}+a}{3x_{n-1}^{2}}, n\geq{1}[/tex]
    Last edited: Oct 29, 2007
  4. Oct 30, 2007 #3


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    I'm actually old enough to remember this. It's been somewhat wisely forgotten. http://www.nist.gov/dads/HTML/cubeRoot.html. You may wish to also check out the Isaac Asimov story, "The Feeling of Power". Kind of haunting, these days.
  5. Oct 30, 2007 #4
    Thanks, now it is coming back!!
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