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The first person to consider the discrepancy of sequences of the type (αnσ)n⩾1 (where 0<σ<1) was H. Behnke[1]. The subject was taken up again by one of the authors of this paper[3], who gave a detailed description of the discrepancy's behaviour if either 0<σ<½ or σ=½ and α2∉Q or σ=½ and α−2∈N. In this paper, we study the case of sequences (α√n)n⩾1 where α>0 and α2∈Q. Both limN→∞¯ N‐1/2ω+(α) and limN→∞¯ N‐1/2ω‐(α) are expressed as maxima of finitely many numbers which involve class numbers of imaginary quadratic fields in many cases.