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 Cardano's "Ars Magna". According to historian of mathematics D.E. Smith, Aryabhata's method for finding the square root was first introduced in Europe by Cataneo in 1546. According to Jeffrey A. Oaks, Arabs used the letter "jīm/ĝīm" (), the first letter of the word “” (variously transliterated as "jaḏr", "jiḏr", "ǧaḏr" or "ǧiḏr", “root”), placed in its initial form () over a number to indicate its square root. The letter "jīm" resembles the present square root shape. Its usage goes as far as the end of the twelfth century in the works of the Moroccan mathematician Ibn al-Yasamin. The symbol '√'