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I'll skip out some tedious bits that I'm confident I have correct and get to the part I'm stuck on

Let L = Q(3^{1/3})

[L:Q] = 3

Clearly [K:L] >1

w is a root of X^{3}-1

So

[K:L] is less than or equal to 3, in particular it is either 2 or 3

Here is where i'm stuck

I tried to show that X^{3}-1 is the min poly of K over L by supposing there exists an a,b in Q such that

(a+b(3^{1/3})) = 1

with a hope of finding a contradiction, but when a=1 this is clearly a root and 1 is an element of L, so this canot be the minimal polynomial of K over L.

Can anyone help me find the minimal polynomial of K over L?

Thanks

Matt

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# Homework Help: Compute the degree of K over Q

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