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Finding real roots of negative numbers (for example, −8−−−√3−83\sqrt[3]{-8})

6 answers

I have a function

g[x_] := (x^3 – x^2)^(1/3)

that I want to plot. The plot I am getting gives me strange results. There is nothing plotted for x < 1, contrary to the results that I can obtain from my calculator. Do you have a idea why? ================= ================= 1 Answer 1 ================= You probably want to use Surd rather than Power. Mathematica normally treats expressions as complex-valued, which may give results differing from most calculators, which are restricted to the reals. Surd is provided to give calculator-like behavior when that is desired. g[x_] := Surd[x^3 - x^2, 3] With[{a = 3}, Plot[g[x], {x, -a, a}]] Perfect thank you and do you know what is the origin of this label "Surd"? – Bendesarts Oct 7 '15 at 19:38 2 @Bendesarts. I believe it is an old word pertaining to the extraction of irrational roots of integers; recall that "absurd" and "irrational" are practically synonyms. – m_goldberg Oct 7 '15 at 19:43 7 Or use CubeRoot. – Daniel Lichtblau Oct 7 '15 at 19:49