The concept of roots is closely related to the topic of exponents, and often appears on the medium and difficult GRE math questions. The formal definition of a root is the following:

The n-th root of a number x is a number r which, when raised to the power of n, equals to x

In other words: rn = x

For example, 2 is a 4th root of 16 because 2⁴ = 16. The number n is called the degree of the root. A root of degree 2 is called a square root, a root of degree 3 is called a cube root, a root of degree 4 is called a fourth root, and so on. In general, a root of degree n is called an nth root. The square root of a number, because it is a concept that is used often in various disciplines, has its own special symbol:

Cubed roots (and, in fact any n-th root, but we'll spare you the details) can also be written using a symbol notation.

So how does this all relate to exponents? Well, roots are treated as special cases of exponentiation, where the exponent is a fraction:

The topic of roots and square roots could be included in the Algebra section of the tutorials, but we are including it here because, often-times, when you are asked a math question on the GRE exam that attempts to measure your knowledge of roots, the question will not include variables such as x or r, but instead will contain only numbers.