36 (number) 36 (number) 36 (thirty-six) is the natural number following 35 and preceding 37. 36 is both the square of six and a triangular number, making it a square triangular number. It is the smallest square triangular number other than one, and it is also the only triangular number other than one whose square root is also a triangular number. It is also a circular number- a square number that ends with the same integer by itself (6×6=36). It is the smallest number "n" with exactly eight solutions to the equation φ("x") = "n". Being the smallest number with exactly nine
Square root of a matrix , then the Jordan decomposition into generalized eigenspaces of can be deduced from the partial fraction expansion of . The corresponding projections onto the generalized eigenspaces are given by real polynomials in . On each eigenspace, has the form as above. The power series expression for the square root on the eigenspace show that the principal square root of has the form "q"("A") where "q"("t") is a polynomial with real coefficients. Another way to find the square root of an "n" × "n" matrix "A" is the Denman–Beavers square root iteration. Let "Y" = "A" and "Z" = "I", where