Euclidean norm calculations arise frequently in scientific and engineering applications. Several approximations for this norm with differing complexity and accuracy have been proposed in the literature. Earlier approaches [1,2,3] were based on minimizing the maximum error. Recently, Seol and Cheun [4] proposed an approximation based on minimizing the average error. In this paper, we first examine these approximations in detail, show that they fit into a single mathematical formulation, and compare their average and maximum errors. We then show that the maximum errors given by Seol and Cheun are significantly optimistic.