nth root

The nth root of a number is a value that, when raised to the nth power, gives that number. It generalizes the square root (n = 2) and cube root (n = 3) to any positive whole number n. The fourth root of 16 is 2, because 2^4 = 16.

The small number n is the index of the root, and it controls how the root behaves. When n is odd, every real number has exactly one real nth root, keeping the sign of the original. When n is even, a positive number has two real roots (the symbol gives the nonnegative principal one) and a negative number has no real nth root at all, since an even power is never negative.

The nth root is exactly the same idea as the exponent 1/n: the nth root of b equals b^(1/n). This link between radicals and fractional exponents lets you apply all the familiar exponent rules to roots, which is often the easiest way to simplify complicated radical expressions.