Algebra I Honors Simplifying Radical Expression Review Worksheet (Quiz and Test Review)
No Calculator. Write your answers in simplest radical form.
Due by Thursday, May 28th.
Simplify the Radical.
Solve Radical Equations. Check for extraneous
1. √726
values.
2. √225
26. √3𝑘 = 3
27. √8 − 2𝑏 = 𝑏
3. 9√343
4. 11√500
5. 14√96
𝑞
28. √ = √2𝑞 + 6
√6
29. √4𝑝 + 4 = √3𝑝 + 13
Simplify the Radical Expression.
6.
7.
30. −3 + √𝑟 + 7 = 2
3
√8
5
√2673𝑑 6 𝑥 6
Simplify the Rational Expression
8. √28𝑦
31.
4
9. √81𝑤 4
18
6𝑥−48
𝑘−9
32. 4𝑘−36
3
10. √704𝑦 6 𝑝4
𝑐 2 +2𝑐−24
33. 𝑐 2 +11𝑐+30
Add or subtract to simplify the radical expression.
11. −√3 − √3 + √27
12. 5√11 − √11 + 4√11
13. 4√2 + 6√2 + 2√32
14. 8√27 − 5√18 − 6√48
15. √63 + √27 − √112 + √12
36.
38. 𝑦 2 +7𝑦+12 ∙ 𝑦+6
39.
40.
19. √176𝑏(−√45𝑏 2 + √28𝑏 3 )
−
21.
22.
23.
24.
25.
√5
5√21𝑛2
5√27𝑛
1+√7ℎ
√5ℎ
1−√3
1−√2
7√5𝑘 4 𝑛4
6√11𝑘 5 𝑛4
12𝑘−30
÷
12
𝑝2 −5𝑝−14
4𝑝
28𝑘−70
12𝑘
÷ (𝑝 − 7)
Simplify the Complex fraction.
+ √7)
Simplify by Dividing. (Remember to rationalize the
denominator)
4√7
∙
36𝑛2 −36
7
9
8𝑐+16
𝑐+2
𝑦 2 +4𝑦−12
1
18. (√3 + √7)(−√3 − √7)
20.
27𝑛2 −27𝑛 7𝑛
37. 𝑐−11 ∙
2
5√7)(−2√11𝑛2
35𝑝2 +6𝑝−8
𝑥−4
Multiply and Divide Rational Expressions
16. −√44 ∙ −2√48
(7√11𝑛2
30𝑝2 +18𝑝−12
35. −𝑥+4
Simplify by Multiplying.
17. (√3 + √5)
34.
41.
42.
4
3 7
+
4 4
5𝑛 1
+
8 5
𝑛2
43. 3
44.
45.
2
8
2 5
9 𝑠+6
+
5
9
12
𝑠2 −
5
12 7
−
7 2
−
2
Add or Subtract the Rational Expressions.
46.
6𝑔
5
4𝑔−2
− 2𝑔−7
−9
𝑞−7
47. 𝑞2 −𝑞−2 − 𝑞2 −𝑞−2
48.
49.
−9
+
𝑘−3
𝑘 2 −4𝑘−32
𝑘 2 −4𝑘−32
2𝑛−8𝑧
2𝑛+4𝑧
2
4𝑛2𝑧
2𝑝3 +3
− 4𝑛2 𝑧 2
6𝑝3
50. 4𝑝5 −8 − 4𝑝5 −8
Rationalize the Denominator. Then simplify.
12
27
51. √50 − √ 8
3
52. √13
53.
54.
55.
56.
57.
20
√10
3√22∙√28
√8∙√77
√75
√2
√10
√6
2
√2
15
∙√6
2
÷ √15
+
12
37
√18
1
58. 5√5 − √45 + 10√5
Solve the absolute Value equations
59. |𝑥 − 5| = 13
60. |4 − 𝑥| = 19
61. |2𝑥 − 7| = 43
62. |3 + 8𝑥| = −1
63. |2𝑥 + 5| − 7 = 22
64. 5 − |𝑥 − 3| = 1
Tricky ones:
65. |4𝑥 − 6| = 𝑥
66. |𝑥| = 𝑥
67. |𝑥| = −𝑥
Equations with squares. Solve for x. Write your
answer in simplest radical form where necessary.
68. (𝑥 − 3)2 = 64
69. (𝑥 + 5)2 = 81
70. (2𝑥 + 7)2 = 25
71. (4𝑥 − 12)2 = 0
72. (𝑥 + 9)2 = −36
73. (𝑥 + 7)2 = 95
74. (𝑥 − 8)2 = 64
75. 𝑥 2 + 6𝑥 + 9 = 16
76. 𝑥 2 + 2𝑥 + 1 = 42
Complete the square. Solve by completing the
square. Write your answer in simplest radical
form.
77. 𝑥 2 + 6𝑥 + 4 = 0
78. 𝑥 2 − 16𝑥 − 17 = 0
79. 𝑥 2 − 4𝑥 − 77 = 0
80. 𝑥 2 + 16𝑥 + 20 = 0
81. 2𝑥 2 − 14𝑥 = −13
True or False:
82. √ 2 =
√37
√2
83. √25 + 36 = √25 + √36
84. √100 − 49 = √100 − √49
85. √8 ∙ √6 = √48