An n-th root of a number r is a number which, if n copies are multiplied together, makes r. It is also called a radical or a radical expression. It is a number k for which the following equation is true:

This is the graph for . It is a square root.
This is . It is a cube root.

(for the meaning of , see Exponentiation.)

We write the nth root of r as .[1] If n is 2, then the radical expression is a square root. If it is 3, it is a cube root.[2][3] Other values of n are referred to using ordinal numbers, such as fourth root and tenth root.

For example, because . The 8 in that example is called the radicand, the 3 is called the index, and the check-shaped part is called the radical symbol or radical sign.

Roots and powers can be changed as shown in .

The product property of a radical expression is the statement that . The quotient property of a radical expression is the statement .[3], b != 0.

Simplifying change

This is an example of how to simplify a radical.


If two radicals are the same, they can be combined. This is when both of the indexes and radicands are the same.[4]


This is how to find the perfect square and rationalize the denominator.


Related pages change

References change

  1. "List of Arithmetic and Common Math Symbols". Math Vault. 2020-03-17. Retrieved 2020-09-22.
  2. Weisstein, Eric W. "nth Root". Retrieved 2020-09-22.
  3. 3.0 3.1 "nth Roots". Retrieved 2020-09-22.
  4. "Add and Subtract Radicals". Retrieved March 14, 2018.