Radicals.

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Presentation transcript:

Radicals

Radicals

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

Examples

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More Examples

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

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

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!!

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

Examples