Mathematics in Ancient and Medieval India c5.s9.16

c5.s9.16

Methods of extraction of square roots (*khai fang*) and cubic roots (*khai li fang*) with the help of abacus or counting boards appear in China in the *Chiu-Chang suan shu* (later half of the 1st century A. D.).¹ Yang Hui (c. 1261 A. D.) explained the methods of root extraction as found in the *Chiu-Chang suan shu* with an example of finding the square root of 71824 in his book, *Hsiang Chieh chiu chang suan fa* (A Detailed Analysis of the Mathematical Methods in the "Nine Chapters"). This gives the various stages on the counting board with the help of a diagram and illustrates the geometrical basis of the method.² In the cube-root method, Liu Hui and Li Shun-feng, commentators in the *Chiu Chang suan shu* both hinted at the use of cubical blocks to demonstrate the process. In Europe the derivation of the square-root method was done possibly from the Euclidean concept (a+b)² = a²+2ab+b².