radical rules
Radical Rules
Root Rules
nth Root Rules
Algebra rules for nth roots are listed below. Radicalexpressions 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.
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Definitions
| Examples
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2. If n is odd then |
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3. If n is even then |
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4. If a ≥ 0 then
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Distributing (a ≥ 0 and b ≥ 0) 1. 2. | Examples
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| Rationalizing the Denominator (a > 0, b > 0, c > 0) | Examples |
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Example
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Careful!! 1. 2. 3. | Examples
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if both b ≥ 0 and bn = a.
because 23 = 8.
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and 
(b ≠ 0)
(m ≥ 0)
See also
nth root, square root rules, distributing rules, absolute value rules, factoring rules
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