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Simplifying Radicals Practice Problems

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Updated on Aug 24, 2011

To review these concepts, go to Simplifying Radicals Study Guide.

Practice

Simplify the radicals.

  1. 12
  2. 49
  3. 81
  4. 500
  5. 144
  6. –√64
  7. 4√4
  8. –2√9
  9. a2
  10. 5√36
  11. 1,600
  12. 8√0
  13. 3n2
  14. 24x5
  15. 0.04
  16. 100x4
  17. –2√4a8
  18. 3√25x2y18
  19. –4√400a6b2
  20. 5√144x4y2
  21. 8
  22. 20
  23. 54
  24. 40
  25. 72
  26. 27
  27. 28
  28. 160
  29. 200
  30. 44
  31. 225
  32. 500
  33. 1,200
  34. 11
  35. 3x2y2
  36. 4b6
  37. 8c4d
  38. 80a2b3c4
  39. 20a5b6c
  40. 500d13

Add and subtract the radicals. Simplify the radical when necessary.

  1. 3√7 + 8√7
  2. 11√3 – 8√3
  3. 5√2 + 6√2 – 3√2
  4. 3√6 + 2√2 – 5√6
  5. 4√a + 13√a
  6. 75 – √20 + 3√5
  7. 9√x – 4√y + 2√x
  8. 12 + 3√3
  9. 2√18 + 6√2
  10. 3√5+ √20 – √7

Multiply and divide the radicals. Simplify the radicals when necessary.

  1. 7√3 · 5√2
  2. –3√5 · 4√2
  3. 3√a · 4√b
  4. 3√10 · 5√10
  5. 4√6 · 5√3

Mixed Practice

Here's a chance to review what you learned.

  1. 20
  2. 4√18
  3. 3√25x6y
  4. 13√5 + 5√13
  5. (6√2)(3√10)
  6. 2√24 + 2√27
  7. 32x4y7z3
  8. 400x4
  9. 5√2 + 7√2(4√3)
  10. 6√3 · 6√3 + 10
  11. (–2√7)2
  12. 2[–4√2(5√5)]

Solutions

  1. 2√3
  2. 7
  3. 9
  4. 10√5
  5. 12
  6. –8
  7. 8
  8. –6
  9. a
  10. 30
  11. 40
  12. 0
  13. n3
  14. 2x26x
  15. 0.2
  16. 10x2
  17. –4a4
  18. 15xy9
  19. –80a3b
  20. 60x2y
  21. 2√2
  22. 2√5
  23. 3√6
  24. 2√10
  25. 6√2
  26. 3√3
  27. 2√7
  28. 4√10
  29. 10√2
  30. 2√11
  31. 15
  32. 10√5
  33. 20√3
  34. prime
  35. xy3
  36. 2b3
  37. 2c22d
  38. 4abc25b
  39. 2a2b35ac
  40. 10d65d
  41. 5a2b
  42. 2√3y
  43. 14
  44. 4√5
  45. 5√2
  46. 2
  47. 14
  48. 2√2a
  49. 11√7
  50. 3√3
  51. 8√2
  52. 2√2 – 2√6
  53. 17√a
  54. 5√3 + √5
  55. 11√x – 4√y
  56. 5√3
  57. 12√2
  58. 5√5 – √7
  59. 35√6
  60. 2√3
  61. –12√10
  62. 2√5
  63. 12√ab
  64. 2√x
  65. 6
  66. 150
  67. 60√2
  68. 2√5
  69. 12√2
  70. 15x3y
  71. no like terms
  72. 36√5
  73. 4√6 + 6√3
  74. 4x2y3z2yz
  75. 20x2
  76. 5√2 – 28√6
  77. 118
  78. 28
  79. –40√10
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