Show that $\sqrt[3]{\sqrt 3+2} +4$ is an algebraic number
2026-04-24 14:34:48.1777041288
How to prove a number is algebraic?
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Standard method: set $x=\sqrt[3]{\sqrt{3}+2}+4$. Now compute $(x-4)^3=\sqrt{3}+2$. So $[(x-4)^3-2]^2=3$ and you're done.