13th 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 13th root of a number is much smaller: a 13th root will have approximately 1/13th the number of digits. Thus, the 13th root
Square root of 2 method of computing square roots, which is one of many methods of computing square roots. It goes as follows: First, pick a guess, ; the value of the guess affects only how many iterations are required to reach an approximation of a certain accuracy. Then, using that guess, iterate through the following recursive computation: The more iterations through the algorithm (that is, the more computations performed and the greater ""), the better approximation of the square root of 2 is achieved. Each iteration approximately doubles the number of correct digits. Starting with the next approximations are The value of was