Algebra I Honors Simplifying Radical Expression Review Worksheet (Quiz and Test Review)
No Calculator. Write your answers in simplest radical form.
Due on Wednesday, June 1st. This will count for 40 points in Class Work.
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
35.
36.
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
∙
36𝑛2 −36
7
9
8𝑐+16
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
27𝑛2 −27𝑛 7𝑛
38. 𝑦 2 +7𝑦+12 ∙ 𝑦+6
18. (√3 + √7)(−√3 − √7)
20.
−𝑥+4
𝑐+2
𝑦 2 +4𝑦−12
1
2
5√7)(−2√11𝑛2
35𝑝2 +6𝑝−8
𝑥−4
37. 𝑐−11 ∙
16. −√44 ∙ −2√48
(7√11𝑛2
30𝑝2 +18𝑝−12
Multiply and Divide Rational Expressions
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
4𝑛2 𝑧 2
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
In class Review (Answers to this portion will be
posted AFTER in class game.
Chapter 12 Review.
86.
87.
𝑥2 +6𝑥+9
4𝑥3
2𝑥2 +12𝑥+18
16𝑥7
𝑡 2 −9𝑡−22
5𝑡−1
𝑣+2
÷ (5𝑡 2 + 9𝑡 − 2)
𝑣−2
88. 2𝑣2 −𝑣−15 − 𝑣2 +2𝑣−15
5
𝑞
2𝑞−27
89. 𝑞+4 = 𝑞−3 + 𝑞2 +𝑞−12
Find the product
90.
24 14 x 6

40
7x2
91. x 2  8 x  15 x 2  2 x  8

x 2  7 x  10 3x 2  9 x
Find the quotient.
92.
4 x 4  20 x 2 16 x 2  112 x

x7
x 2  49
93.
94.
24
6

3
5 x 25 x 2
2𝑥 2 −9𝑥−5
5−𝑥
÷
2𝑥 2 +7𝑥+3
𝑥+3
Solve.
95. A kayaker travels 9 miles up a river with a
current of 1.25 miles per hour. He then
travels 15 miles back down the river. If the
kayaker can paddle at 3.75 mph in still
water, how long is the kayakers’ trip?
Find the sum.
96.
11 4

2x 7x
97.
5 x3

x2 x 1
Find the difference
98.
x2
x  6x  9
2

x  5 2x

8x
x6
99.
Solve.
100.
2x 
101.
3x  4
2

x2 x2
x  2 2x
18

 2
x  4 x  1 x  5x  4
Simplify.
102.
x 1
x  2 x  15
2
𝑥2 −64
4𝑥2 −7𝑥+3
𝑥+8
3𝑥−3
Simplify.
4𝑥 2
103.
6√
104.
(2 − 4√3)
1
3
2
3𝑛2
Answer Key:
1. 11√6
2. 15
3. 63√7
4. 110√5
5. 56√6
6. 2
5
36. 4𝑛+4
37.
72
𝑐−11
𝑦−2
38. 𝑦 2 +7𝑦+12
39.
40.
3𝑘
7
𝑝+2
4𝑝
8
41. 5
25𝑛+8
7. 3𝑑𝑥 √11𝑑𝑥
42.
8. 2√7𝑦
9. 3w
43. -20
10. 4𝑦 2 𝑝 3√11𝑝
11. √3
12. 8√11
13. 18√2
14. −15√2
15. −√7 + 5√3
16. 16√33
17. 8 + 2√15
18. −10 − 2√21
19. −12𝑏√55𝑏 + 8𝑏 2 √77
20. −154𝑛2 + 17𝑛√77 − 35
21.
22.
23.
4√35
5
√7𝑛
3
√5ℎ+ℎ√35
5ℎ
24. −1 − √2 + √3 + √6
25.
7√55𝑘
40𝑛2
5𝑠+111
44. 45𝑠2 −108
25
45. − 28
46.
12𝑔2 −62𝑔+10
10𝑔−35
𝑞+2
47. − 𝑞2 −𝑞−2
𝑘−12
48. 𝑘 2 −4𝑘−32
−3
49. 𝑛2 𝑧
50.
51.
52.
−4𝑝3 +3
𝑝5 −8
−11√6
20
√39
13
53. 2√10
54. 3
55.
56.
5√15
2
5√2
2
57. 3√2
31. 𝑥−8
58. 4√5
59. {-8,18}
60. {-15,23}
61. {-18,25}
62. {}
63. {-17,12}
64. {-1,7}
32. 4
65. {5 , 2}
33. (𝑐+5)
66. All non-negative numbers
67. All negative numbers and 0
68. {-5,11}
69. {-14,4}
66𝑘
26. {3}
27. {-4,2}
28. {-36/11 }
29. {9}
30. {18}
3
1
(𝑐−4)
6𝑝+6
34. 7𝑝+4
35. -1
6
70. {-6,-1}
71. {3}
72. {}
73. {−√95 − 7, √95 + 7}
74. {0,16}
75. {-7,1}
76. {−√42 − 1, √42 − 1}
77. {−√5 − 3, √5 − 3}
78. {-1,17}
79. {-7,11}
80. {−2√11 − 8, 2√11 − 8}
−√23+7 √23+7
, 2 }
2
81. {
82. True
83. False
84. False
85. True
Answers to Remaining 19 questions will be
posted after in-class game.