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 is the unique positive square root of the positive operator "A""A", and "U" is defined by . If "A" is not invertible, then it still has a polar composition in which "P" is defined in the same way (and is unique). The unitary operator "U" is not unique. Rather it is possible to determine a "natural" unitary operator as follows: "AP" is a unitary operator from the range of "A" to itself, which can be extended by the identity on the kernel of "A". The resulting unitary operator "U" then yields the polar decomposition of "A". By Choi's result, a