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 arithmetic–geometric mean inequality for two variables and, as noted above, is the basis of the Ancient Greek understanding of "Heron's method". Another method of geometric construction uses right triangles and induction: can, of course, be constructed, and once has been constructed, the right triangle with 1 and for its legs has a hypotenuse of . The Spiral of Theodorus is constructed using successive square roots in this manner. 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