Let L/F be a Galois quadratic extension such that F contains a primitive n-th root of 1. Let N = L(${alpha}^{{frac{1}{n}}$) where ${alpha}{in}L{ast}$. We show that if $N_{L/F}({alpha});{in}L^n{cap}F$, and [N : L] = m, then $G(N/ F) {simeq}D_m$ or generalized quaternion group whether $N_{L/F}({alpha});{in};F^n;or;{ otin}F^n$, respectively.