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 2 p. 18). This proof constructively exhibits a discrepancy between and any rational. "Proof": For the given equation, there are only six possible combinations of oddness and evenness for whole-number values of formula_18 and formula_19 that produce a whole-number value for formula_24. A simple enumeration of all six possibilities shows why four of these six are impossible. Of the two remaining possibilities, one can be proven to not contain any solutions using modular arithmetic, leaving the sole remaining possibility as the only one to contain solutions, if any. The fifth possibility (both formula_18 and formula_19 odd and formula_24 even) can be