>>58
That is a good question. Pi is not the root of any "polynomial" equation where the polynomials have powers of x that are fractions, either positive or negative.
For radical exponents, I believe the question is open. That means we don't know the answer.
If you allow *arbitrary* exponents, pi is a root of a zillion different equations. For example, pi is a root of the equation x^q - 2 = 0, where q = log(2)/log(pi).
If you allow the "polynomials" to have infinitely many terms, you can find equations of which pi is a root. For example, it is the smallest positive root of
x - x^3 / 6 + x^5 / 120 - x^7 / 5040 + ... . But this isn't a polynomial.
I hope this does more to clear up the situation than it does to confuse it.