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Math Help - Finding Dimensions And Bases

  1. #1
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    Finding Dimensions And Bases

    OK, I'm so lost. If someone could give me an explanation as to how to do this, I'd appreciate it:

    Find a dimension and basis for the following:

    [Q(sqrt(3), sqrt(5)) : Q(sqrt(15))]

    [Q(sqrt(2), cubert(2), 4thrt(2)) : Q]

    Any help would be appreciated. This is confusing the crap out of me.
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  2. #2
    Senior Member
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    Quote Originally Posted by mathematicalbagpiper View Post
    OK, I'm so lost. If someone could give me an explanation as to how to do this, I'd appreciate it:

    Find a dimension and basis for the following:

    [Q(sqrt(3), sqrt(5)) : Q(sqrt(15))]
    Since sqrt(15)/sqrt(3)=sqrt(5), Q(sqrt(3), sqrt(5)) over Q(sqrt(15)) is the same with Q(sqrt(3), sqrt(15)) over Q(sqrt(15)). Now the basis you have is {1, sqrt(3)}.

    [Q(sqrt(2), cubert(2), 4thrt(2)) : Q]

    Any help would be appreciated. This is confusing the crap out of me.
    Hint: Q(sqrt(2), cubert(2), 4thrt(2)) over Q is the same with Q(cubert(2), 4thrt(2)) over Q.
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