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Lesson37

Lesson37 - Lesson 37 Examine the following 4 9 = 23 = 6...

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1 Lesson 37 Sections 7.3 & 7.4 Examine the following: 4 9 2 3 6 4 9 36 6 = = = = Since both equal 6, the expressions are equal. Conclusion: 4 9 4 9 = Likewise: 2 4 4 16 2 2 4 4 16 = = = = Since both equal 2, the expressions are equal. Conclusion: 4 16 4 16 = These observations lead to two very important rules: the Product and Quotient Rules for Radicals. Product Rule for Radicals: n n n ab b a = Quotient Rule for Radicals: n n n b a b a = Caution: These rules only apply when the indices (plural of index) are equal! Use the rules above (if possible) to multiply, divide, or otherwise simplify. 1. = ) 6 )( 13 ( 3 3 2. 2 3 4 t = 3. 2 3 2 3 x x - + =

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2 4. = 2 25 x 5. = 3 6 27 2 a 6. = 5 80 7. ( ) ( ) = 3 3 x The product rule can also be used to simplify a radical by using factoring. Look at the following example. 20 4 5 4 5 2 5 = = = To simplify a radical with index n (using factoring or the product rule), use the following steps. 1.
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Lesson37 - Lesson 37 Examine the following 4 9 = 23 = 6...

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