Nth root

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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 . If n is 2, then the radical expression is a square root. If it is 3, it is a cube root. 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 . 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.

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

Related pages
 Geometric mean
 Rationalization (mathematics)
 Square number

References

Category:Mathematics