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 of 2 method of computing square roots, which is one of many methods of computing square roots. It goes as follows: First, pick a guess, ; the value of the guess affects only how many iterations are required to reach an approximation of a certain accuracy. Then, using that guess, iterate through the following recursive computation: The more iterations through the algorithm (that is, the more computations performed and the greater ""), the better approximation of the square root of 2 is achieved. Each iteration approximately doubles the number of correct digits. Starting with the next approximations are The value of was