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5.6 Radical Expressions Rationalizing the denominator Like radical expressions Conjugates

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Product Property of Radicals If you have the same index, then you can multiply the radicands.

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Product Property of Radicals Also, go the other way, the simplify radical expressions

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Simplify

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Quotient Property of Radicals Quotients can be broken apart.

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Some rules about Radicals Reduce them to the lowest index.

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Some rules about Radicals Radicals can not have fractions in them. This is called Rationalizing the denominator.

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Some rules about Radicals Radicals can not be in the denominator. No tents in the basement.

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Simplify

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Multiply Radicals You can only multiply radicals if they have the same index.

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Adding and Subtract Radicals If radical are to the same index and have the same radicand, then they are like radical expressions. Like radicals can be added or subtracted.

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Simplify Simplify radicals first.

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Simplify Simplify radicals first.

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Simplify Simplify radicals first.

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Simplify Simplify radicals first.

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Multiply Radicals Remember foiling

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Multiply Radicals Remember foiling

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Multiply Radicals Remember foiling

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Multiply Radicals Remember foiling

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Simplify

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Conjugate You can not have radicals in the denominator. We have to use the conjugate to rational the denominator in fractions.

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Conjugate You can not have radicals in the denominator. We have to use the conjugate to rational the denominator in fractions.

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Conjugate You can not have radicals in the denominator. We have to use the conjugate to rational the denominator in fractions.

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Simplify Use the conjugate

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Simplify Use the conjugate

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Homework Page 254 – 255 #15 – 49 odd 57,58

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Homework Page 254 – 256 #16 – 48 even 75 - 82

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