Radical Rules
Root Rules
nth Root Rules
Algebra rules for nth
roots are listed below.
Radical expressions can be rewritten using exponents, so the rules
below are a subset of the exponent
rules.
For all of the following, n is an integer and n ≥ 2.

Definitions
1. if both b ≥ 0 and b^{n} = a.

Examples
because 2^{3} = 8.

2. If n is odd then .


3. If n is even then .


4. If a ≥ 0 then .

and

Distributing (a ≥ 0 and b ≥ 0)
1.
2. (b ≠ 0)

Examples

3. ( multiplied by itself n times equals a)


4. (m ≥ 0)


Rationalizing the Denominator
(a > 0, b > 0, c > 0) 
Examples 




Example

Careful!!
1.
2.
3. 
Examples

See also
nth root, square
root rules, distributing
rules, absolute value rules,
factoring rules
