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 2 by 2 matrix use the simplified formula where "a" = ±√"A" and "d" = ±√"D"; which, for the various sign choices, gives four, two, or one distinct matrices, if none of, only one of, or both "A" and "D" are zero, respectively. Because it has duplicate eigenvalues, the 2×2 identity matrix formula_10 has infinitely many symmetric rational square roots given by where is any Pythagorean triple—that is, any set of positive integers such that formula_12 In addition, any non-integer, irrational, or complex values of "r, s, t" satisfying formula_13 give square root matrices. The identity matrix also has infinitely many non-symmetric square roots.