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 number, and quadratic irrational for a proof for all non-square natural numbers.) The square root function maps rational numbers into algebraic numbers (a superset of the rational numbers). For all real numbers "x", For all nonnegative real numbers "x" and "y", and The square root function is continuous for all nonnegative "x" and differentiable for all positive "x". If "f" denotes the square root function, its derivative is given by: The Taylor series of about "x" = 0 converges for ≤ 1 and is given by The square root of a nonnegative number is used in the definition of Euclidean