I was just going through some of the primality test algorithms. It seems that the regular one  loop up to square root of $n$  has running time $O(n^{1/2})$.Is $O(n^{1/2})$ exponential? And is exponential time better than polynomial always?
Is $O(n^{1/2})$ exponential? Is $O(n)$ better than $O(n^{1/2})$?
complexity theory;time complexity