Radical Functions Unit 3 Parts of a Radical

Radicals Principal root—positive root (for even indexes) For a radical to be completely simplified,

Rationalizing the denominator Multiply by a sq. rt. that will give you a perfect

Radical Operations +, -, X, / Radicals Treat Radicals like variables Must have like

More Radical Operations When multiplying— remember “inside #s with inside #s and outside #s

Dividing Radicals When dividing, you can not have a radical left in the denominator

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Radical Functions Unit 3

Parts of a Radical

Radicals Principal root—positive root (for even indexes) For a radical to be completely simplified, (A) all perfect nth root factors should be removed from underneath the radical, (B) no fractions left underneath the radical, and (C) no radicals left in the denominator All even powered variables are perfect squares— the square root is the ½ power.

Simplify, if possible

Rationalizing the denominator Multiply by a sq. rt. that will give you a perfect sq. in the denominator so that you can eliminate the radical

Simplify, if possible

Simplifying Higher Order Radicals

Simplify

Examples

More Examples

Radical Operations +, -, X, / Radicals Treat Radicals like variables Must have like radicals to add or subtract Like radicals are the same radicand 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

Simplify completely