Thread: 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.

Originally Posted by mathematicalbagpiper

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.