There is an undocumented function Internal`RadicalMemberQ
which takes two arguments. But whatever input I try for the two arguments, it seems to crash the kernel (Mathematica 10.3 on Mac OS X). Can anyone guess what the function does based on the name of this function?
Internal`RadicalMemberQ[Sqrt[x], x] (*Kernel crash*)
Internal`RadicalMemberQ[2, x] (*Kernel crash*)
Internal`RadicalMemberQ[a x^2 + 2 x - b, x] (*Kernel crash*)
Internal`RadicalMemberQ["Saul Alinsky"]
? $\endgroup$Internal`RadicalMemberQ[Pi, Sqrt[2]] (*False*)
Internal`RadicalMemberQ[2, Sqrt[2]] (*True*)
$\endgroup$