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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 bn = a.

Examples

because 23 = 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

 


  this page updated 28-jul-14
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes