# A ramification problem

Suppose $K$ be a number field containing no root of $1$ except $\pm 1$, $n\geq 3$ be a positive integer, $a\in K$ is not an $m$th-power for any $m|n$, Since we know well about the ramification of those primes outside $n$, so I want to know: does all prime ideals of $K$ dividing $n$ ramify in $K(\sqrt[n]{a})$?

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Sometimes they do, sometimes they don't. Question like these are better suited for mse. –  Franz Lemmermeyer Jan 17 at 14:26