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 produce another whole-number square, even when the equation is not in its simplest form. "Proof": Assume formula_40 is rational. Therefore, But the lemma proves that the sum of two identical whole-number squares cannot produce another whole-number square. Therefore, the assumption that formula_40 is rational is contradicted. formula_40 is irrational. Q. E. D. One-half of , also the reciprocal of , approximately , is a common quantity in geometry and trigonometry because the unit vector that makes a 45° angle with the axes in a plane has the coordinates This number satisfies One interesting property of is as follows: since This