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Question: show that the algebraic closure of the padic field qp...

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Show that the algebraic closure of the p-adic field Qp has infinite degree? Equivalently, you can show that p-adic field admits finite extensions of arbitrary degree by basically showing that x^n-p is irreducible over Qp for all n bigger than 0.

Please show your work! (please don't copy from other websites).

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