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:

(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

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

## References

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