Key Concept A radical with an index of 3, such as 27−−√3

3 root of 27, is read as the cube root of 27. A radical with an index of 4, such as 16−−√4

4 root of 16, is read as the fourth root of 16.

An index of 5 is read as a fifth root, and so on.

This familiar lingo is generalized for any index by calling it an nth root Opens in modal popup window .

If a and b are real numbers, n is a positive integer greater than 1, and an=b

a to the power of n equals b, then a is an nth root of b. The nth root of b is written b√n

n root of b, where n is the index of the radical and b is the radicand. The radicand can be a real number or an algebraic expression.

The index tells you how many matching factors it takes in the radicand to become a root.

For example:

16−−√4=2

The fourth root of 16 is 2

.

16−−√4=2⋅2⋅2⋅2−−−−−−−−√4=(2)4−−−√ 4=2