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 The method uses the same iterative scheme as the Newton–Raphson method yields when applied to the function y = "f"("x") = "x" − "a", using the fact that its slope at any point is "dy"/"dx" = ""("x") = 2"x", but predates it by many centuries. The algorithm is to repeat a simple calculation that results in a number closer to the actual square root each time it is repeated with its result as the new input. The motivation is that if "x" is an overestimate to the square root of a nonnegative real number "a" then "a"/"x" will be an