The following properties (rules) are used when working with radicals of all indices.
Let x and y be real numbers, variables, or algebraic expressions that yield real numbers,
and let m and n be positive integers.
| Property (Rule): |
Symbolism: |
In plain English ... |
Root to the Root Power
(Inverse) |
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An n-root radical raised to the n-power returns the radicand (the inside). [Tthe inverse property for roots and powers.] |
| Product Rule |
|
When multiplying, and the roots, n, are the same, keep root, multtply inside. |
| Quotient Rule |
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When dividing, and the roots are the same, keep the index and divide the values inside. |
| Radical to a Power |
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When raising a radical to a power, keep the index, and raise the inside to the power. |
| Root of a Root |
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When taking the root of a root, multiply the indices, and keep the radicantd. |
| Even Root Rule |
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For even roots, the root raised to the same power = absolute value of the inside. This keeps only 1 positive root as the solution (principal root).. |
| Odd Root Rule |
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For odd roots, the root raised to the same power gives the inside radicand.
It is the inverse property at work. |
Properties of Radicals (Rules):
