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 Square root In mathematics, a square root of a number "a" is a number "y" such that ; in other words, a number "y" whose "square" (the result of multiplying the number by itself, or ) is "a". For example, 4 and −4 are square roots of 16 because . Every nonnegative real number "a" has a unique nonnegative square root, called the "principal square root", which is denoted by , where √ is called the "radical sign" or "radix". For example, the principal square root of 9 is 3, which is denoted by = 3, because and 3 is