Observations on Square Roots of Leftins

  1. Not all integers have square roots in L0 (or Lf).
  2. The integers which have square roots in a composite number base is the intersection of integers which have square roots in the bases of its factors.
  3. The precision of a square root is not always the same as the precision of the number. There may be several ambiguous digits.
  4. Square roots always come in pairs of additive inverses (except zero which is its own additive inverse).
  5. The number of square roots of an integer is 2 raised to the power of the number of unique prime factors of the number base.
Table of Square Roots
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© Scott Sherman 1999