1. What does it mean when a radical does not have an index? Is the expression equal to the radicand? Explain.
2. Where would radicals come in the order of operations? Explain why.
3. Every number will have two square roots. What is the principal square root?
4. Can a radical with a negative radicand have a real square root? Why or why not?
For the following exercises, simplify each expression.
5. 256
6. 256
7. 4(9+16)
8. 289−121
9. 196
10. 1
11. 98
12. 6427
13. 581
14. 800
15. 169+144
16. 508
17. 16218
18. 192
19. 146−624
20. 155+745
21. 150
22. 10096
23. (42)(30)
24. 123−475
25. 2254
26. 324405
27. 361360
28. 1+35
29. 1−178
30. 416
31. 3128+332
32. 5243−32
33. 45154125
34. 33−432+316
For the following exercises, simplify each expression.
35. 400x4
36. 4y2
37. 49p
38. (144p2q6)21
39. m25289
40. 93m2+27
41. 3ab2−ba
42. 16n442n
43. 49x225x3
44. 344z+99z
45. 50y8
46. 490bc2
47. 14d32
48. q2363p
49. 1−3x8
50. 121d420
51. w2332−w2350
52. 108x4+27x4
53. 2+2312x
54. 147k3
55. 125n10
56. 36q342q
57. 361m281m
58. 72c−22c
59. 324d2144
60. 324x6+381x6
61. 416x4162x6
62. 364y
63. 3128z3−3−16z3
64. 51,024c10
65. A guy wire for a suspension bridge runs from the ground diagonally to the top of the closest pylon to make a triangle. We can use the Pythagorean Theorem to find the length of guy wire needed. The square of the distance between the wire on the ground and the pylon on the ground is 90,000 feet. The square of the height of the pylon is 160,000 feet. So the length of the guy wire can be found by evaluating 90,000+160,000. What is the length of the guy wire?
66. A car accelerates at a rate of 6−t4 m/s2 where t is the time in seconds after the car moves from rest. Simplify the expression.
For the following exercises, simplify each expression.
67. 4−28−16−221
68. 831423−1623
69. a2c−3mn3⋅m2c4a−7n−2
70. a−ca
71. 128yx64y+4y
72. (100b3250x2)(125x7b)
73. 64+256364+4256
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College Algebra.Provided by: OpenStaxAuthored by: OpenStax College Algebra.Located at: https://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1/Preface.License: CC BY: Attribution.