Square root of 3 billion digits. The fraction (…) for the square root of three can be used as an approximation. Despite having a denominator of only 56, it differs from the correct value by less than (approximately ). The rounded value of 1.732 is correct to within 0.01% of the actual value. Archimedes reported , accurate to (six decimal places) and (four decimal places), respectively. It can be expressed as the continued fraction , expanded on the right. It can also be expressed by generalized continued fractions such as which is evaluated at every second term. The following nested square expressions converge to
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 '√'