Mathematics in Ancient and Medieval India c5.s14.25

c5.s14.25

¹ Since Aa² + 1 = b², we have √A = √((b² - 1)/(a²)) = b/a √(( 1 - 1/(b²) )). If b is large, b/a is a close approximation to √A. The error is less than 1/(2x² √N) and greater than 1/2xy. This can be verified at once by writing √A = y/x √(1 - 1/(y²)) and expanding the right hand side by the binomial theorem.