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 the name of Hippasus of Metapontum is often mentioned. For a while, the Pythagoreans treated as an official secret the discovery that the square root of two is irrational, and, according to legend, Hippasus was murdered for divulging it. The square root of two is occasionally called "Pythagoras' number" or "Pythagoras' constant", for example by . There are a number of algorithms for approximating , which in expressions as a ratio of integers or as a decimal can only be approximated. The most common algorithm for this, one used as a basis in many computers and calculators, is the Babylonian