Square root any nonnegative number, then the principal square root of −"x" is The right side (as well as its negative) is indeed a square root of −"x", since For every non-zero complex number "z" there exist precisely two numbers "w" such that : the principal square root of "z" (defined below), and its negative. There are two complex numbers that square to a given arbitrary non-zero imaginary number formula_11 with real formula_12 where the two-digit pattern {3, 6} repeats over and over again in the partial denominators. Since , the above is also identical to the following generalized continued fractions: The
Square root (1.41421356...). The Rhind Mathematical Papyrus is a copy from 1650 BC of an earlier Berlin Papyrus and other textspossibly the Kahun Papyrusthat shows how the Egyptians extracted square roots by an inverse proportion method. In Ancient India, the knowledge of theoretical and applied aspects of square and square root was at least as old as the "Sulba Sutras", dated around 800–500 BC (possibly much earlier). A method for finding very good approximations to the square roots of 2 and 3 are given in the "Baudhayana Sulba Sutra". Aryabhata in the "Aryabhatiya" (section 2.4), has given a method for finding the