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WorksheetsLessons 10-2 & 10-3 Simplifying Radicals
Total questions: 110
Worksheet time: 14hrs 33mins
Name
Class
Date
1.
√121v
a)
11v
b)
11√v
c)
11v√v
d)
√11v
2.
-4√1000
a)
-400
b)
-40
c)
-400√100
d)
-40√100
3.
√75x²
a)
5x²√3
b)
5x
c)
5x√3x
d)
5x√3
4.
√45x⁴y⁷
a)
3x²y³√5
b)
9x²y³√5y
c)
3x²y³√5y
d)
3x⁴y⁷
5.
√512a10
a)
8a⁵√4
b)
16a⁵√2
c)
16a¹⁰√2
d)
16a⁵√a
6.
√500x8y2
a)
10x⁴y√5
b)
10x⁴y²√5
c)
50x⁴y
d)
100x⁴y√5
7.
√36n4
a)
6n
b)
6n⁴
c)
6n²√2
d)
6n²
8.
-3√80a7
a)
4a³√5a
b)
-12a³√5a
c)
-3a³√5a
d)
-48a³√5a
9.
2√18a6b2
a)
3a³b√2
b)
6a³b²√2
c)
6a³b√2
d)
2a³b√2
10.
√98a20c15
a)
7c√a¹⁰c⁷
b)
7a¹⁰c⁷√2
c)
49a¹⁰c⁷√2c
d)
7a¹⁰c⁷√2c
11.
Simplify the following radical: √24
a)
2√6
b)
4√6
c)
2√12
d)
3√8
12.
Simplify the following radical: √300
a)
3√10
b)
2√150
c)
100√3
d)
10√3
13.
Simplify the following radical: √275
a)
5√5
b)
5√11
c)
11√5
d)
5√55
14.
Simplify the following radical: √150
a)
5√15
b)
5√2
c)
5√6
d)
15√5
15.
Simplify 4√75
a)
4√5
b)
12√5
c)
20√3
d)
7√3
16.
Simplify the following radical: √32
a)
3√2
b)
4√8
c)
16√2
d)
4√2
17.
3√700
a)
21√10
b)
3√7
c)
10√7
d)
30√7
18.
Simplify the following radical: 2√24
a)
4√6
b)
2√6
c)
24√2
d)
4√4
19.
5√80
a)
20√5
b)
4√5
c)
5√20
d)
4√5
20.
True or False: The following list contains only perfect squares.
1, 4, 9, 27, 81, 100
1, 4, 9, 27, 81, 100
a)
True
b)
False
21.
Simplify the radical - 3√27
a)
9
b)
9√3
c)
3√9
d)
3
22.
Simplify the radical - 10√20
a)
5√20
b)
20√5
c)
4√5
d)
40√5
23.
Simplify the radical - 6√90
a)
10√8
b)
10√18
c)
18√10
d)
18√9
24.
What is the simplified form of √140
a)
4√35
b)
10√14
c)
2√70
d)
2√35
25.
In simplest radical form, -5√75 is equivalent to:
a)
5√3
b)
-15√5
c)
√3
d)
-25√3
26.
Simplify:
3√250
3√250
a)
15√10
b)
5√250
c)
8√10
d)
15√3
27.
Simplify:
√72
a)
√72
b)
2√2
c)
6√2
d)
4√18
28.
The number under the radical sign or square root sign is called the ______.
a)
radical sign
b)
radicand
c)
factor
d)
exponent
29.
In simplest radical form,
√75 is equivalent to
√75 is equivalent to
a)
25√3
b)
25√3
c)
5√3
d)
3√5
30.
a)
xy√y
b)
x²y²√y
c)
xy√xy
d)
2x2y√y
31.
a)
x3√x
b)
7x√x2
c)
x6√x
d)
√x
32.
a)
x4y4√y
b)
72xy
c)
xy√y
d)
x2y3√x2
33.
a)
y
b)
y2
c)
√y
d)
y√0
34.
a)
y2z10√xy
b)
20yz√xy
c)
xy2z10√y
d)
yz6√xy2z2
35.
The square roots of all perfect squares are___________?
a)
integers or whole numbers
b)
irrational
c)
fractions
d)
divisible by 2
36.
Simplify √45x⁴y⁷
a)
3x²y³√5
b)
9x²y³√5y
c)
3x²y³√5y
d)
3x⁴y⁷
37.
Simplify:
√(a2)
√(a2)
a)
a
b)
a2
c)
a.5
d)
already simplified
38.
Simplify: √20a²
a)
2a√5
b)
4a√5
c)
5a√2
d)
2a²√5
39.
√100y4
a)
10√y2
b)
10y√y
c)
10y
d)
10y2
40.
Simplify: √(49x3)
a)
7x2√x
b)
7x√x
c)
7√x3
d)
7x
41.
Simplify the radical...
√20a²b⁴
a)
2ab²√5
b)
4ab²√5
c)
5ab²√2
d)
2a²b²√5
42.
a)
y2z10√xy
b)
20yz√xy
c)
xy2z10√y
d)
yz6√xy2z2
43.
What is the square root symbol called?
a)
Radicand
b)
Radical
c)
The house
d)
It doesn't have a name
44.
The product of a number multiplied by itself is?
a)
Square Root
b)
Rectangle
c)
Circle
d)
Perfect Square
45.
Simplify
a)
12√15/15
b)
4√15/5
c)
4/5
d)
Can't Simplify
46.
Simplify
a)
√5
b)
0.2
c)
√5/5
d)
Can't Simplify
47.
Simplify
a)
12√2/2
b)
6
c)
6√2
d)
Can't Simplify
48.
Simplify
a)
√.66
b)
√6/3
c)
2
d)
Can't Simplify
49.
Simplify
a)
√15/√9
b)
√15/3
c)
5
d)
Can't Simplify
50.
Simplify
a)
√245/5
b)
3√5/√5
c)
3
d)
Can't Simplify
51.
Simplify
a)
10/11 f√2
b)
10∙11∙f5
c)
10/11√f10
d)
10f5 /11
52.
Simplify:
a)
1/5
b)
20/100
c)
2/10
d)
1/√25
53.
In the picture, the "3" is called...
a)
the index
b)
the radical sign
c)
the radicand
d)
none
54.
Rationalize the denominator.
a)
A
b)
B
c)
C
d)
D
55.
a)
A
b)
B
c)
C
d)
D
56.
a)
A
b)
B
c)
C
d)
D
57.
a)
A
b)
B
c)
C
d)
D
58.
Simplify:
a)
2
b)
4√3
c)
2√3
d)
4
59.
Simplify
a)
√5
b)
0.2
c)
√5/5
d)
Can't Simplify
60.
The number inside the radical is called...
a)
the index
b)
the radical sign
c)
the radicand
d)
none
61.
Simplify:
a)
b)
c)
d)
62.
To multiply radicals, they must have the same radicand
a)
True
b)
False
63.
Simplify:
a)
2
b)
4√3
c)
2√3
d)
4
64.
Simplify:
a)
(√2)/3
b)
5√2
65.
Simplify:
a)
√10
b)
√40/2
c)
2√5/√2
d)
10
e)
None of the above
66.
Simplify the radical.
a)
-19
b)
-180
c)
No Real Number
d)
19
67.
Simplify the radical.
a)
5
b)
1/5
c)
1/625
d)
25
68.
Simplify the radical.
a)
b)
c)
d)
69.
a)
b)
c)
d)
70.
Simplify the radical. Assume all variables are positive.
a)
x4y8
b)
x3y10
c)
x6y5
d)
x3y5
71.
Simplify the radical.
a)
50m5n9
b)
10m5n9
c)
50m8n16
d)
10m8n16
72.
Simplify the radical.
a)
b)
c)
d)
73.
Simplify the radical.
a)
b)
c)
d)
74.
Simplify the radical. Assume the variable is positive.
a)
b)
c)
d)
75.
a)
A
b)
B
c)
C
d)
D
76.
a)
A
b)
B
c)
C
d)
D
77.
What is the opposite of squaring a number?
Example: Opposite of 32
Example: Opposite of 32
a)
Find the Square Root
b)
Dividing the number
c)
Multiplying the number
d)
Cubing the number
78.
What do all these numbers have in common?
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
a)
They are perfect squares
b)
They are even numbers
c)
They are adorable
d)
They can all be divided by 2
79.
Simplify the expression:
a)
-15 + 8√9
b)
9
c)
2 + 8√3 + 6√6
d)
9 + 14√3
80.
Simplify:
a)
A
b)
B
c)
C
d)
D
81.
Add: 4√7 - 10 √7 + 7√7
a)
-6√7
b)
14√7
c)
-3√14
d)
√7
82.
Simplify: 2√40 - 3√10
a)
5√10
b)
√10
c)
-√30
83.
4√3 - √12
a)
√6
b)
2√3
c)
√2
d)
√5
84.
√5 × √10
a)
50
b)
2√5
c)
5√2
d)
5√10
85.
a)
A
b)
B
c)
C
d)
D
86.
a)
(21-7√15) ∕ -6
b)
(21 - √95) ∕ -6
c)
(21 + 7√15) ∕ 24
d)
(-21 - 7√15) ∕ 24
87.
a)
-2x - x√3
b)
2x + x√3
c)
2x - √(3x)
d)
2x + √(3x)
88.
a)
7√3
b)
Can't Simplify
c)
6√15
d)
6√3
89.
a)
8√6
b)
8√12
c)
12√6
d)
12√12
90.
a)
A
b)
B
c)
C
d)
D
91.
Simplify:
a)
A
b)
B
c)
C
d)
D
92.
Simplify:
a)
A
b)
B
c)
C
d)
D
93.
Simplify:
a)
A
b)
B
c)
C
d)
D
94.
Simplify the expression:
a)
√2 - 3√3
b)
2√-59
c)
-2√2 - 3√3
d)
-3.782
95.
Perform the operation. Express your answer in simplest form.
a)
54√14 - 12√33
b)
18√14 - 6√33
c)
-3√6
d)
3√14 - 2√33
96.
√8 - 6√2
a)
-4√2
b)
2√2
c)
-6√6
d)
-6√10
97.
(-2√7)(3√28)
a)
-6√14
b)
6√13
c)
-84
d)
-78
98.
√3 × √15 =
a)
3√5
b)
5√3
c)
2√7
d)
√17
99.
Simplify -2√10 ⋅ 3√20
a)
-60√2
b)
10√2
c)
√30
d)
-6√200
100.
2√5 - √5 + 4√5 + √3
a)
6√5 + √3
b)
5√5 + √3
c)
6√5
d)
6√3
101.
The expression 5+√2 is the conjugate of
a)
√5-√2
b)
√2-5
c)
2-√5
d)
5-√2
102.
a)
A
b)
B
c)
C
d)
D
103.
Simplify
-2√5+3√20
-2√5+3√20
a)
-2√8
b)
-6√36
c)
-6√-12
d)
4√5
104.
Simplify
3√2 - 3√18
3√2 - 3√18
a)
-4√8
b)
4√9-6√3
c)
5√12
d)
-6√2
105.
Simplify:
6√2 ⋅5√14
6√2 ⋅5√14
a)
32√7
b)
60√7
c)
2√7
d)
30√7
106.
Simplify the radical expression:
a)
A
b)
B
c)
C
d)
D
107.
Simplify the radical expression:
a)
A
b)
B
c)
C
d)
D
108.
Simplify the radical expression:
a)
A
b)
B
c)
C
d)
D
109.
Simplify the expression:
a)
-15 + 8√9
b)
9
c)
2 + 8√3 + 6√6
d)
9 + 14√3
110.
The process of eliminating radicals from the denominator of a fraction is called ______________.
a)
division
b)
rationalizing the denominator
c)
rationalizing the numerator
d)
factoring
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