We show that there is a consistent choice of square root in a finite field \(\mathbb{F}_{p^k}\) for odd prime \(p \neq 1\) and \(k\neq 0\) if and only if \(k\) is odd.

We show that there is a consistent choice of square root in a finite field \(\mathbb{F}_{p^k}\) for odd prime \(p \neq 1\) and \(k\neq 0\) if and only if \(k\) is odd.