 # Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 8 Rational Exponents, Radicals, and Complex Numbers.

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Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 8 Rational Exponents, Radicals, and Complex Numbers

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 3 Radical Equations and Problem Solving 1.Use the power rule to solve radical equations. 8.6

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 4 Power Rule for Solving Equations If both sides of an equation are raised to the same integer power, the resulting equation contains all solutions of the original equation and perhaps some solutions that do not solve the original equation. That is, the solutions of the equation a = b are contained among the solutions of a n = b n, where n is an integer. Radical equation: An equation containing at least one radical expression whose radicand has a variable.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 5 Example Solve. a.b. Solution a. Check True b. Check True

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 6 Example Solve. Solution Check: The number 41 checks. The solution is 41.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 7 Example Solve. Solution Check: True. The solution is  4.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 8 Example Solve. Solution Check: False, so 6 is extraneous. This equation has no real number solution.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 9 Example Solve. Solution Check: The number 4 checks. The solution is 4.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 10 Example Solve. Solution Square both sides. Use FOIL. Subtract x from both sides. Factor. Use the zero-factor theorem. Subtract 7 from both sides.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 11 continued Checks False. True. Because 2 does not check, it is an extraneous solution. The only solution is 9.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 12 Example Solve. Solution Check This solution does not check, so it is an extraneous solution. The equation has no real number solution.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 13 Example Solve Solution Check The solution set is 13.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 14 Example Solve Solution Check There is no solution.