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Homework Help: Intermediate fields

  1. May 21, 2010 #1
    How do I go about showing a field is intermediate between two others?

    For example I'm trying to do this question:


    But first of all I'm trying to find the degree of the extension [F:Q[i.rt(6)]]

    How can I show that Q[i.rt(6)] is an intermediate field?
  2. jcsd
  3. May 21, 2010 #2


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    Staff Emeritus
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    It's obviously contains Q because, well it contains Q. It's contained in [tex]\mathbb{Q}[\sqrt{2}-i\sqrt{3}][/tex] because [tex](\sqrt{2}-i\sqrt{3})^2=2-2i\sqrt{6}-3[/tex] (try to work out the details if that doesn't make it obvious).
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