EXAMPLE 13 Reducing the Index of a Radical Simplify SOLUTION 8242016 Algebra

# Example 13 reducing the index of a radical simplify

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EXAMPLE 13 Reducing the Index of a Radical Simplify: . SOLUTION 8/24/2016 Algebra and Trigonometry 76/171 Check Point 13 Simplify: . Blitzer Bonus || A Radical Idea: Time Is Relative The Persistence of Memory (1931), Salvador Dali:. © 2011 MOMA/ARS. What does travel in space have to do with radicals? Imagine that in the future we will be able to travel at velocities approaching the speed of light (approximately 186,000 miles per second). According to Einstein’s theory of special relativity, time would pass more quickly on Earth than it would in the moving spaceship. The special-relativity equation gives the aging rate of an astronaut, R a , relative to the aging rate of a friend, R f , on Earth. In this formula, v is the astronaut’s speed and c is the speed of light. As the astronaut’s speed approaches the speed of light, we can substitute c for v . Close to the speed of light, the astronaut’s aging rate, R a , relative to a friend, R f , on Earth is nearly 0. What does this mean? As we age here on Earth, the space traveler would barely get older. The space traveler would return to an unknown futuristic world in which friends and loved ones would be long gone. CONCEPT AND VOCABULARY CHECK Fill in each blank so that the resulting statement is true. 8/24/2016 Algebra and Trigonometry 77/171 1. The symbol is used to denote the nonnegative, or __________, square root of a number. 2. because _____ = 64. 3. _____ 4. The product rule for square roots states that if a and b are nonnegative, then = _____. 5. The quotient rule for square roots states that if a and b are nonnegative and = _____. 6. = _____ 7. ___ = _____ 8. The conjugate of 7 + is __________. 9. We rationalize the denominator of by multiplying the numerator and denominator by __________. 10. In the expression , the number 3 is called the _____ and the number 64 is called the __________. 11. because _____ = −32. 12. If n is odd, = _____. If n is even, = _____. 13. = _____ 14. = (___) 3 = ___ EXERCISE SET P.3 Practice Exercises Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. 1. 8/24/2016 Algebra and Trigonometry 78/171 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. 13. 14. 15. 16. 17. 18. 8/24/2016 Algebra and Trigonometry 79/171 19. 20. 21. 22. Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 8/24/2016 Algebra and Trigonometry 80/171 In Exercises 33–44, add or subtract terms whenever possible. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. In Exercises 45–54, rationalize the denominator. 45. 46. 47. 48. 8/24/2016 Algebra and Trigonometry 81/171 49.  #### You've reached the end of your free preview.

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