Formulas For The Square Root Modulo p

A method of constructing specific polynomial representations $f(x)$ over the finite field ${\mathbb{F}}_p$ of the square roots function modulo a prime $p = 2^kn + 1$,$n$odd,ispresented\mathrm{.}Theformulasforthecases$k = 2$,$3$and$4$ are given.