Can the Euclidean distance function be computed using only XOR's

Question

The Eulidean distance function $d$ of $x$ and $y$ is given by:

$ d(x,y)=\sqrt{x^2-y^2} $

Let us assume that $x$ and $y$ are fixed-point numbers, or $x,y$ are element of some subfield $f_n$ of $F_p$. We could even assume that $x,y$ have precision $n$ decimal digits. Any facilitating representations of rational or real values $x,y$ that carries "enough" information is good. $x,y$ could also be assumed to be only positive.

Can the Euclidean distance function be computed using only XOR's? If this cannot be achieved, what other boolean functions would be needed?