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 there is a matrix and a diagonal matrix such that . This happens if and only if has "n" eigenvectors which constitute a basis for . In this case, can be chosen to be the matrix with the "n" eigenvectors as columns, and thus a square root of is where is any square root of . Indeed, For example, the matrix formula_14 can be diagonalized as , where giving the square root When is symmetric, the diagonalizing matrix can be made an orthogonal matrix by suitably choosing the eigenvectors (see spectral theorem). Then the inverse of is simply the transpose,