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 5 of five can be used. Despite having a denominator of only 72, it differs from the correct value by less than (approx. ). As of December 2013, its numerical value in decimal has been computed to at least ten billion digits. 1. This irrationality proof for the square root of 5 uses Fermat's method of infinite descent: 2. This irrationality proof is also a proof by contradiction: It can be expressed as the continued fraction The convergents and semiconvergents of this continued fraction are as follows (the black terms are the semiconvergents): Convergents of the continued fraction are colored red;