Question: Let n be a positive integer. Then f = x n - 2 is irreducible over Q by the Eisenstein criterion or by the fact

Let n be a positive integer. Then f = xn - 2 is irreducible over Q by the Eisenstein criterion

or by the fact that 2 is not an n-th power in Q for n > 1, we

proved, that a polynomial of the form xn - a is either irreducible or has a root.

(a) Determine a splitting field L of f over Q.

(b) Show that when n is prime, we have [L : Q] = n(n - 1).

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