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Radicals

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Radicals

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**Radicals Principal root—positive root (for even indexes)**

For a radical to be completely simplified, all perfect nth root factors should be removed from underneath the radical, no fractions left underneath the radical and no radicals left in the denominator All even powered variables are perfect squares—the sq. rt is ½ the power

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Examples

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More Examples

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**Rationalizing the denominator**

Multiply by a root that will give you a perfect nth root in the denominator in order to eliminate the radical

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**Radical Operations +, -, X, / Radicals Treat Radicals like variables**

Must have like radicals to add or subtract Like radicals are the same radicand and the same index

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**More Radical Operations**

When multiplying—remember “inside #s with inside #s and outside #s with outside #s” Multiply then simplify or simplify then multiply You must foil if you multiply a binomial by another binomial!!

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Dividing Radicals When dividing, you can not have a radical left in the denominator in the final answer. If there is only 1 term, then we rationalize. If there are 2 terms, then multiply by the conjugate

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Examples

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Dividing and Simplifying Just as the root of a product can be expressed as the product of two roots, the root of a quotient can be expressed as the quotient.

Dividing and Simplifying Just as the root of a product can be expressed as the product of two roots, the root of a quotient can be expressed as the quotient.

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