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Determine the degree of the splitting field.

  1. Nov 2, 2009 #1
    1. The problem statement, all variables and given/known data
    What is the degree of [tex]t^5-6[/tex] over [tex]\mathbb{Q}[/tex]?


    2. Relevant equations and the attempt at a solution
    Let [tex]z=e^{\frac{2\pi i}{5}}[/tex] and let [tex]\alpha = \sqrt[5]{6}[/tex]. (The real one). Then the roots of [tex]t^5-6[/tex] are

    [tex]\alpha z^0, \alpha z^1, \alpha z^2, \alpha z^3, \alpha z^4.[/tex]

    So we want to find:

    [tex][Q(e^{\frac{2\pi i}{5}}, \sqrt[5]{6}):Q][/tex]

    This is where I get confused. A small hint would be nice.
     
  2. jcsd
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