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Radicals.  Principal root—positive root (for even indexes)  For a radical to be completely simplified, all perfect n th root factors should be removed.

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Presentation on theme: "Radicals.  Principal root—positive root (for even indexes)  For a radical to be completely simplified, all perfect n th root factors should be removed."— Presentation transcript:

1 Radicals

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3  Principal root—positive root (for even indexes)  For a radical to be completely simplified, all perfect n th 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

4 Examples

5 More

6 More Examples

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

8 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

9 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!!

10 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

11 Examples


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