Square root of 2 the square root of two, with a reasonable small denominator, the fraction (≈ 1.4142857) is sometimes used. The sequence in the OEIS gives the numerical value for the square root of two, truncated to 65 decimal places: The Babylonian clay tablet YBC 7289 (c. 1800–1600 BC) gives an approximation of in four sexagesimal figures, , which is accurate to about six decimal digits, and is the closest possible three-place sexagesimal representation of : Another early close approximation is given in ancient Indian mathematical texts, the Sulbasutras (c. 800–200 BC) as follows: "Increase the length [of the side] by its third
Square root of a matrix but if the process converges, the matrix formula_26 converges quadratically to a square root , while formula_27 converges to its inverse, . Yet another iterative method is obtained by taking the well-known formula of the Babylonian method for computing the square root of a real number, and applying it to matrices. Let "X" = "I", where "I" is the identity matrix. The iteration is defined by Again, convergence is not guaranteed, but if the process converges, the matrix formula_29 converges quadratically to a square root "A". Compared to Denman–Beavers iteration, an advantage of the Babylonian method is that only one