# Homework Help: Determine the degree of the splitting field.

1. Nov 2, 2009

### futurebird

1. The problem statement, all variables and given/known data
What is the degree of $$t^5-6$$ over $$\mathbb{Q}$$?

2. Relevant equations and the attempt at a solution
Let $$z=e^{\frac{2\pi i}{5}}$$ and let $$\alpha = \sqrt[5]{6}$$. (The real one). Then the roots of $$t^5-6$$ are

$$\alpha z^0, \alpha z^1, \alpha z^2, \alpha z^3, \alpha z^4.$$

So we want to find:

$$[Q(e^{\frac{2\pi i}{5}}, \sqrt[5]{6}):Q]$$

This is where I get confused. A small hint would be nice.