ON THE EXACT DEGREE OF Q(√a1,√a2,...,√al) OVER Q

Let S = {a(1),a(2),...,a(l)} be a finite set of non-zero integers. In this paper, we give an exact formula for the degree of the multi-quadratic field Q(root a(1),root a(2),...,root a(l)) over Q. To do this, we compute the relative density of the set of prime numbers p for which all the a(i)'s are simultaneously quadratic residues modulo p in two ways.