nth root
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:
![](http://up.wiki.x.io/wikipedia/commons/thumb/6/6c/Squareroot-0-9-metapost.svg/220px-Squareroot-0-9-metapost.svg.png)
![](http://up.wiki.x.io/wikipedia/commons/thumb/4/41/Cube-root_function.svg/220px-Cube-root_function.svg.png)
(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
changeThis 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
changeReferences
change- ↑ "List of Arithmetic and Common Math Symbols". Math Vault. 2020-03-17. Retrieved 2020-09-22.
- ↑ Weisstein, Eric W. "nth Root". mathworld.wolfram.com. Retrieved 2020-09-22.
- ↑ 3.0 3.1 "nth Roots". www.mathsisfun.com. Retrieved 2020-09-22.
- ↑ "Add and Subtract Radicals". mathbitsnotebook.com. Retrieved March 14, 2018.