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 a "positive-semidefinite matrix" has precisely one positive-semidefinite square root, which can be called its "principal square root". While the square root of a nonnegative integer is either again an integer or an irrational number, in contrast an "integer matrix" can have a square root whose entries are rational, yet not integer. For example, the matrix formula_8 has the non-integer square root formula_9 as well as the integer square root matrix formula_10. The 2×2 identity matrix is another example. A 2×2 matrix with two distinct nonzero eigenvalues has four square roots. More generally, an matrix with "distinct nonzero eigenvalues" has 2