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 formulas that give up to four square roots, if the matrix has any roots. If is a diagonal "n" × "n" matrix, one can obtain a square root by taking a diagonal matrix , where each element along the diagonal is a square root of the corresponding element of . If the diagonal elements of "D" are real and non-negative, and the square roots are taken with non-negative sign, the matrix will be the principal root of . If a matrix is idempotent, one of its square roots is the matrix itself. An "n" × "n" matrix is diagonalizable if