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Chapter 8

Chapter 8. Section 5. More Simplifying and Operations with Radicals. Simplify products of radical expressions. Use conjugates to rationalize denominators of radical expressions. Write radical expressions with quotients in lowest terms. 8.5. 2. 3.

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Chapter 8

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  1. Chapter 8 Section 5

  2. More Simplifying and Operations with Radicals Simplify products of radical expressions. Use conjugates to rationalize denominators of radical expressions. Write radical expressions with quotients in lowest terms. 8.5 2 3

  3. More Simplifying and Operations with Radicals The conditions for which a radical is in simplest form were listed in the previous section. A set of guidelines to use when you are simplifying radical expressions follows: Slide 8.5-3

  4. More Simplifying and Operations with Radicals (cont’d) Slide 8.5-4

  5. Objective 1 Simplify products of radical expressions. Slide 8.5-5

  6. Find each product and simplify. EXAMPLE 1 Multiplying Radical Expressions Solution: Slide 8.5-6

  7. Find each product and simplify. EXAMPLE 1 Multiplying Radical Expressions (cont’d) Solution: Slide 8.5-7

  8. Find each product. Assume that x≥ 0. EXAMPLE 2 Using Special Products with Radicals Solution: Remember only like radicals can be combined! Slide 8.5-8

  9. Using a Special Product with Radicals. Example 3 uses the rule for the product of the sum and difference of two terms, Slide 8.5-9

  10. Find each product. Assume that EXAMPLE 3 Using a Special Product with Radicals Solution: Slide 8.5-10

  11. Objective 2 Use conjugates to rationalize denominators of radical expressions. Slide 8.5-11

  12. The results in the previous example do not contain radicals. The pairs being multiplied are called conjugates of each other. Conjugates can be used to rationalize the denominators in more complicated quotients, such as Use conjugates to rationalize denominators of radical expressions. Using Conjugates to Rationalize a Binomial Denominator To rationalize a binomial denominator, where at least one of those terms is a square root radical, multiply numerator and denominator by the conjugate of the denominator. Slide 8.5-12

  13. Simplify by rationalizing each denominator. Assume that EXAMPLE 4 Using Conjugates to Rationalize Denominators Solution: Slide 8.5-13

  14. Simplify by rationalizing each denominator. Assume that EXAMPLE 4 Using Conjugates to Rationalize Denominators (cont’d) Solution: Slide 8.5-14

  15. Objective 3 Write radical expressions with quotients in lowest terms. Slide 8.5-15

  16. Write in lowest terms. EXAMPLE 5 Writing a Radical Quotient in Lowest Terms Solution: Slide 8.5-16

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