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
Nth root positive "n"th root, called the principal "n"th root, which is written formula_6. For "n" equal to 2 this is called the principal square root and the "n" is omitted. The "n"th root can also be represented using exponentiation as "x". For even values of "n", positive numbers also have a negative "n"th root, while negative numbers do not have a real "n"th root. For odd values of "n", every negative number "x" has a real negative "n"th root. For example, −2 has a real 5th root, formula_29 but −2 does not have any real 6th roots. Every non-zero number "x",