# Series expansion: Taylor series takes huge amount of time

I'm working on a notebook, trying to expand the root of a cubic polynomial in Taylor series. When I type:

Series[(Sqrt[46656 a^2 - 864 (3 2^(1/3) a^(2/3) + 2 a B)^3] + 216 a)^(1/3) , {a, 0, 2}]


Mathematica takes an indefinite amount of time and I am forced to halt execution. After this occurs, even simple functions like Exp[x] will not compute and I have to restart the kernel.

Am I doing something wrong here? My computer is a month old, so I know the problem isn't old hardware.

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Works for me, but takes a bit more than two minutes on an i7-2820QM. –  Yves Klett Nov 4 '13 at 17:56
Do you really need an exact, symbolic result? It is likely to be huge so it may not be useful to you. You could convert the input to inexact numbers to a certain precision and work with that. –  Szabolcs Nov 4 '13 at 18:00
Series[N[(Sqrt[46656 a^2 - 864 (3 2^(1/3) a^(2/3) + 2 a bb)^3] + 216 a)^(1/3), 30], {a, 0, 2}] –  Szabolcs Nov 4 '13 at 18:00
You're not doing anything incorrect here. It seems that the Series code is using a fairly high order in some internal computations. I need to check whether there is solid reason for that, or whether it needs to be tamed to some extent. –  Daniel Lichtblau Nov 4 '13 at 18:33
If you take @Szabolcs advice: Series[(Sqrt[46656 a^2 - 864 (3 2^(1/3) a^(2/3) + 2 a B)^3] + 216 a)^(1/3) // N, {a, 0, 2}] works very quickly –  Yves Klett Nov 4 '13 at 18:47