Simplify Each Radical Expression

Name Class Date

Unit 3 Review

Radicals & Rationals Lesson 10-2 Simplify each radical expression. 27 25 50 15. 16. 17. 81 4 9 72 19. 20. 27 . 3 18. 25· 4 50 44x4 3c2 23. 45 · 18 21. 22. 11 27

Use the formula d = 1.5h to estimate the distance d in miles to a horizon when h is the height of the viewer's eyes above the ground. Round your answer to the nearest mile.

24. Find the distance you can see to the horizon from the top of a building that is 355 ft high.

25. Find the distance you can see to the horizon from an airplane that is 36,000 ft above the ground.

26. Find the distance you can see to the horizon from 15 ft above the ground.

Lesson 10-3 Simplify each radical expression. 27. 75 - 4 75 28. 5 ( 20 - 80 ) 29. 6 ( 6 - 3)

30. 3 300 + 2 27 31. 32. 8 - 4 2 5 2 ·3 50

2 z3 34. 5 +1 5 -1 33. ( )( ) 35. ( 3 + 2) 5z 1 2 3 +1 36. 37. 38. 2 +1 2 - 2 2 +1

Lesson 10-4 Solve each radical equation. Check your solution.

41. 3x + 4 =1 42. 6= 8x - 4 43. 2x= 14 x - 6

44. 2x+ 5 = 3 x + 1 45. 2x= 6 x + 4 46. 5x+ 11 = 7 x - 1

47. 3x- 2 = x 48. x+7 = x + 1 x + 9 49. x +3 = 5 Write and solve a radical equation for each situation.

50. What is the diameter of a circular livestock pen if the area is 450 m2?

51. On a roller coaster ride, your speed in a loop depends on the height h of the preceding hill and the radius of the loop in feet. The equation v=8 h - 2 r gives the velocity v in feet per second of a car at the top of the loop. Suppose a loop has a radius of 25 ft and you want the car to have a velocity of 25 ft/s at the top of the loop. How high should the preceding hill be?

Lesson 10-5 Find the domain of each function. Describe the transformation. Then sketch the function.

52. y= x + 5 53. y= x - 2 54. y= x +1

55. y= x - 4 56. y= x - 3 57. y= x + 6

Find the constant of variation k for each inverse variation.

46. y = 10 when x = 7 47. y = −8 when x = 12 48. y = 0.2 when x = 4

Each pair of points is on the graph of an inverse variation. Find the missing value.

49. (5.4, 3) and (2, y) 50. (x, 4) and (5, 6) 51. (3, 6) and (9, y)

52. (100, 2) and (x, 25) 53. (6, 1) and (x, −2) 54. (8, y) and (−2, 4)

Do the data in each table represent a direct variation or an inverse variation? Write an equation to model the data in each table. 55. 56. 57. x y x y x y –4 –10 3 8 9 6 5 8 6 4 12 8 20 2 12 2 21 14

Write an inverse variation to model each situation. Then answer the question. 58. Two rectangular fields have the same area. One measures 75 yd by 60 yd. If the other has a length of 72 yd, what is its width?

59. Kevin is training to run in a half marathon. Initially, he could run 6 miles per hour for 2 hours. Two months later he ran the same distance in 1 hour and 45 minutes. What is his new speed?

Write each expression in simplest form. Assume that all variables are positive.

4 3 15 1 1 1 骣- 3 5 31. 812 32. 364 36 4 33. 琪x y 桫

1 3 16 骣 - 1 1 4 8 15 - -9 6 34. 琪x y 35. (8x y - 9) 3 36. (-27x y )3 桫 1 1 1 16 - 骣81y 4 37. (-32x-10 y 15 )5 38. (32x20 y- 10 ) 5 39. 琪桫16x12 1 6 2 14 2 骣16x 3 x 40. 琪 41. 5 5 42. 桫81y18 3 x5

Describe the transformation of parent function f (x).

56. h(x) = f(x  1) 57. g(x) = f(x) + 2 58. k(x) = f(x)

1 59. g(x) = 3.4f (x) 60. k(x) = f(x) 61. h(x) = f(x) 2

Describe the transformation of f (x) that produces g (x).

62. f(x) = 2x  1 63. f(x) = 4x 64. f(x) = 3x 1 1 g(x) = x + 1 g(x) = 2x  g(x) = (3x  1) 2 2