# Finding Dimensions And Bases

• Feb 28th 2010, 12:13 PM
mathematicalbagpiper
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.
• Mar 1st 2010, 12:17 AM
aliceinwonderland
Quote:

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)}.

Quote:

[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.