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 and 1, "ω", "ω", ... "ω" are the "n"th roots of unity. For example, the four different fourth roots of 2 are In polar form, a single "n"th root may be found by the formula Here "r" is the magnitude (the modulus, also called the absolute value) of the number whose root is to be taken; if the number can be written as "a+bi" then formula_97. Also, formula_98 is the angle formed as one pivots on the origin counterclockwise from the positive horizontal axis to a ray going from the origin to the number; it has the properties that formula_99