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
Methods of computing square roots that formula_211 is as small as possible. A completely different method for computing the square root is based on the CORDIC algorithm, which uses only very simple operations (addition, subtraction, with bitshift and table lookup to implement multiplication). The square root of "S" may be obtained as the output formula_197 using the hyperbolic coordinate system in vectoring mode, with the following initialization: Quadratic irrationals (numbers of the form formula_216, where "a", "b" and "c" are integers), and in particular, square roots of integers, have periodic continued fractions. Sometimes what is desired is finding not the numerical value of a square