EXERCISES For more exercises, see Extra Skill and Word Probism Practice Practice and Problem Solving Practice by Example Find all the real square roots of each number. 4. 64 Example 1 1. 225 2. 0.0049 3. -121 169 for (page 370) GO Find all the real cube roots of each number. Help 8. 0.000343 5. -64 6. 0.125 7. - 216 Find all the real fourth roots of each number. 12, 10,000 11. 0.0081 81 9. 16 10. - 16 Ravin Example 2 Find each real-number root. (page 370) 16. V0.36 13. V36 14. - V36 15. V-36 17. - V 64 18. V-64 19. -V81 20. V -81 Example 3 Simplify each radical expression. Use absolute value symbols when needed. (page 371) 21. V16x2 22. V0.25x6 23. Vx8y 18 24. V 646 48 25. V-64a3 V 26. V/276 mod 27. Vx 8 y 12 NUs 28. V 32y10 Example 4 Geometry The formula for the volume of a sphere is V = 3mrs. Find the radius to (page 371) the nearest hundredth of a sphere with each volume. 29. 10 in.3 30. 20 ft 3 31. 0.45 cm 3 32. 0.002 mm 3 B Apply Your Skills Find the two real-number solutions of each equation. 33. x2 = 100 34. x4 = 1 35. x2 = 0.25 36. x4 = 37. Arrange the numbers V -64, -V-64, V64, and 64 in order from least to greatest. 38. Boat Building Boat builders share an old rule of thumb for sailboats. The maximum speed K in knots is 1.35 times the square root of the length L in feet of the boat's waterline. a. A customer is planning to order a sailboat with a maximum speed of 8 knots. How long should the waterline be? b. How much longer would the waterline have to be to achieve a maximum speed of 10 knots? Simplify each radical expression. Use absolute value symbols when needed. 39. V0.125 40. 3 8 41. V0.0016 43. V 16c4 44. V81x3 y6 42. V 256 al-World Connection 45. V144x3 y475 47. V -20 46. 5 20 waterline of a boat is the 48. 5 k 15 49. V-K15 rsection of the boat with 50. V (x + 3)2 urface of the water when 51. V(x + 1) 4 52. Wx2n oat is at rest. 53. Wx4n 54. V xon 55. Open-Ended Find three radical expressions that simplify to -2x2. Chapter 7 Radical Functions and Rational Exponents