13th root 13th root of a 100-digit number. All world records for mentally extracting a 13th root have been for numbers with an integer root. 13th root Extracting the 13th root of a number is a famous category for the mental calculation world records. The challenge consists of being given a large number (possibly over 100 digits) and asked to return the number that, when taken to the 13th power, equals the given number. For example, the 13th root of 8,192 is 2 and the 13th root of 96,889,010,407 is 7. Extracting the 13th root has certain properties. One is that the
Square root of a matrix a "positive-semidefinite matrix" has precisely one positive-semidefinite square root, which can be called its "principal square root". While the square root of a nonnegative integer is either again an integer or an irrational number, in contrast an "integer matrix" can have a square root whose entries are rational, yet not integer. For example, the matrix formula_8 has the non-integer square root formula_9 as well as the integer square root matrix formula_10. The 2×2 identity matrix is another example. A 2×2 matrix with two distinct nonzero eigenvalues has four square roots. More generally, an matrix with "distinct nonzero eigenvalues" has 2