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
Nth root algorithm Nth root algorithm The principal "n"th root formula_1 of a positive real number "A", is the positive real solution of the equation (for integer "n" there are "n" distinct complex solutions to this equation if formula_3, but only one is positive and real). There is a very fast-converging "n"th root algorithm for finding formula_1: A special case is the familiar square-root algorithm. By setting "n" = 2, the "iteration rule" in step 2 becomes the square root iteration rule: Several different derivations of this algorithm are possible. One derivation shows it is a special case of Newton's method (also called