Six proofs are given for the fact that for each integer n [greater than or equal to] 2, the nth root function, viewed as a function from the set of non-negative real numbers to itself, is not linear. If p is a prime number, then [Zeta]/p[Zeta] is characterized, up to isomorphism, as the only integral domain D of characteristic p such that D admits a pth root function D [right arrow] D which is linear. The first part of this note could find classroom use in courses on precalculus or calculus; the second part, in courses on abstract algebra.