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
Integer square root which makes a general multiplication step unnecessary. Integer square root In number theory, the integer square root (isqrt) of a positive integer "n" is the positive integer "m" which is the greatest integer less than or equal to the square root of "n", For example, formula_2 because formula_3 and formula_4. One way of calculating formula_5 and formula_6 is to use Newton's method to find a solution for the equation formula_7, giving the iterative formula The sequence formula_9 converges quadratically to formula_5 as formula_11. It can be proven that if formula_12 is chosen as the initial guess, one can stop as