I want to show when $x^3-p \in \Bbb{Q}_p[x]$ for $p=2,3$ splits completely over $\mathbb{Q}_3$(p^(1/3)) and $\mathbb{Q}_2$(p^(1/3))(so its the splitting field) and when it doesn't split.
2026-04-03 11:44:32.1775216672
Show that $x^3-p \in \Bbb{Q}_p[x]$ for $p=2,3$ splits completely or doesnt over $\mathbb{Q}_3$(p^(1/3)) and $\mathbb{Q}_2$(p^(1/3))
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