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 square roots. Such a matrix, , has a decomposition where is the matrix whose columns are eigenvectors of and is the diagonal matrix whose diagonal elements are the corresponding eigenvalues . Thus the square roots of are given by , where is any square root matrix of , which, for distinct eigenvalues, must be diagonal with diagonal elements equal to square roots of the diagonal elements of ; since there are two possible choices for a square root of each diagonal element of , there are 2 choices for the matrix . This also leads to a proof of the