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Chapter 8 Sections 6 and 7: Solving Radical Equations and Evaluating Rational Exponents

Chapter 8 Sections 6 and 7: Solving Radical Equations and Evaluating Rational Exponents. In this section, we will… Solve equations that contain radical expressions Evaluate expression that contain rational exponents.

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Chapter 8 Sections 6 and 7: Solving Radical Equations and Evaluating Rational Exponents

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  1. Chapter 8 Sections 6 and 7: Solving Radical Equations and Evaluating Rational Exponents • In this section, we will… • Solve equations that contain • radical expressions • Evaluate expression that contain • rational exponents Notice all of the computations, theoretical scribblings, and lab equipment, norm. Yes, curiosity killed these cats.

  2. Solving Radical Equations: 1. Isolate one radical expression on one side of the equation 2. Apply the Power Rule (power = index of radical) 3. Solve the resulting equation (If it still contains a radical, go back to step #1.) 4. Check your potential solution(s) …but applying the power rule can yield additional solutions… • Warning: Be sure to check your potential solution. • A potential solution that fails to check can be a result of: • an incorrect solution that must be fixed or • an extraneous solution that must be discarded Solution set: Solution set:

  3. Examples: Find the real solutions. Check your result(s). checks When checking our potential solution(s), we will take only the primary root.

  4. Examples: Find the real solutions. Check your result(s). checks

  5. Examples: Find the real solutions. Check your result(s). checks

  6. Examples: Find the real solutions. Check your result(s). checks

  7. Evaluating Rational Exponents: Examples: Simplify each expression.

  8. Evaluating Rational Exponents: Examples: Simplify each expression.

  9. Evaluating Rational Exponents: Examples: Simplify each expression. and

  10. Independent Practice You learn math by doing math. The best way to learn math is to practice, practice, practice. The assigned homework examples provide you with an opportunity to practice. Be sure to complete every assigned problem (or more if you need additional practice). Check your answers to the odd-numbered problems in the back of the text to see whether you have correctly solved each problem; rework all problems that are incorrect. Read pp. 685-692 and 696-700 Homework: pp. 692-695 #3, 25, 27, 29, 33, 47, 103, 104 pp. 700-702 #11, 13, 21-45 odds, 112

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