Question

does square 256 represent the positive square root of 256

Answer 1

normally we use wats called the principal squar root or the positive squar root more oftern then the negative root

techniclly $\sqrt{256}$=-16 and +16
so the answer is no

Answer 2

It represents both of them, until it appears in a problem or exercise where there is some reason to discard one or the other.