and consider continued radicals of form limn→∞ Sn = √ a1, a2, a3, . . . . Convergence criteria for continued radicals are given in [2], and [3]. We consider the sets S(M) of real numbers which are representable as a continued radical whose terms a1, a2, . . . are all from a finite set M = {m1,m2, . . . ,mp} ⊆ N where 0 < m1 < m2 < · · · < mp. For any nonnegative number n, √ n, n, n, . . . conve...