Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Choose the answer which is equivalent to the given radical.
1)
3–216
1)
A)
Not a real number
B)
–6
C)
6
D)
–36
2)
–3–27
2)
A)
–3
B)
Not a real number
C)
3
D)
9
C
3)
327
3)
A)
–3, 3
B)
3
C)
Not a real number
D)
9
B
4)
64
4)
A)
–8, 8
B)
Not a real number
C)
4096
D)
8
D
B
5)
–36
5)
A)
–1296
B)
Not a real number
C)
–6
D)
6
6)
–25
6)
A)
–625
B)
Not a real number
C)
5
D)
–5
B
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
7)
Tell whether the statement is true or false. If it is false, give the correct answer. Explain
your answer. The easiest way to simplify the expression 7
4–8 is to multiply both the
numerator and denominator by 4–8.
7)
8)
Tell whether the statement is true or false. If it is false, give the correct answer. Explain
your answer. The easiest way to simplify the expression 35
3 is to multiply both the
numerator and denominator of 35
33 by 33.
8)
Provide an appropriate response.
9)
If there any way you can think of to check whether or not your simplified expression is
equivalent to the original radical expression?
9)
C
10)
A student tries to solve x +6=x+9 by squaring both sides and gets x +6= x +81.
Why is this not correct?
10)
11)
To rationalize the denominator of an expression such as 3
11, we multiply both the
numerator and the denominator by 11. By what number are we actually multiplying the
given expression, and what property of real numbers justifies the fact that our result is
equal to the given expression?
11)
12)
True or false? 4+16 =4+16
12)
13)
Give the definition or an example of the following word or phrase: Like radicals
13)
14)
Tell whether the statement is true or false. If it is false, give the correct answer. Explain
your answer. The easiest way to simplify the expression 2
27 is to multiply both the
numerator and denominator of 2
27 by 27.
14)
15)
Can 3–6 exist as a real number?
15)
16)
Explain how radical denominators are rationalized.
16)
17)
What are the common errors one might make in simplifying radical expressions?
17)
Provide the proper response.
18)
Explain why 3–11 and –311 represent the same number.
18)
19)
Summarize the guidelines to follow when simplifying radical expressions.
19)
Provide the proper response.
20)
If p is a prime number, is p in simplified form? Explain.
20)
21)
What are conjugate expressions? Give an example.
21)
Provide the proper response.
22)
How many square roots does any positive number have?
22)
23)
Tell whether the statement is true or false. If it is false, give the correct answer. Explain
your answer. The easiest way to simplify the expression 3 2
49 is to multiply both the
numerator and denominator of 32
349 by 349.
23)
24)
Can x + 2 = – x have a solution? Why or why not?
24)
Provide the proper response.
25)
Can a represent a negative real number?
25)
26)
True or false? 4·9=4·9
26)
27)
Describe some situation in which it would be important to be able to simplify radical
expressions.
27)
28)
What is wrong with the shown first step in the solution process for
10x + 3 = –3x – 8: 10x + 3 =3x + 8?
28)
Provide the proper response.
29)
How many real number cube roots does any negative number have?
29)
30)
Consider the following “solution.” WHAT WENT WRONG? Give the correct solution set.
2x –7+8= 0
2x –7= –8Subtract 8.
2x –7=64 Square both sides.
2x =71 Add 7.
x =71
2Divide by 2.
The solution set is 71
2.
30)
Provide the proper response.
31)
Give the definition or an example of the word Radicand.
31)
32)
Tell whether the statement is true or false. If it is false, give the correct answer. Explain
your answer. The easiest way to simplify the expression 6
5+2 is to multiply both the
numerator and denominator by 5–2.
32)
33)
Explain why A2 A when A is negative.
33)
34)
Explain why the equation x2=64 has two real number solutions, while the equation
x=8 has only one real number solution.
34)
35)
What value of x will make the following equation true. Explain your answer.
3x – 5 + –9x + 15 = 0
35)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Rationalize the denominator. Assume that all variables represent positive real numbers.
36)
7p
36)
A)
7 p
B)
49 p
p
C)
7
p
D)
7 p
p
Perform the indicated operations. Assume that all variables represent nonnegative real numbers.
37)
527x2z+3x 108z
37)
A)
33x 3z
B)
33 3z
C)
(5 27z+18 3z)x
D)
18x 3z
Find the root.
38)
–31000
38)
A)
10
B)
100
C)
–10
D)
Not a real number
C
Perform the indicated operation and express the answer in simplest form.
39)
(35–33)(325 +315 +39)
39)
A)
8
B)
2
C)
2+345 –375
D)
2+ 2325 + 2 15
B
Solve the equation.
40)
3x + 1 = 3 +x – 4
40)
A)
{–1}
B)
C)
{–5, –8}
D)
{5, 8}
D
Perform the indicated operations. Assume that all variables represent nonnegative real numbers.
41)
74x7–5x4x3
41)
A)
124x3
B)
2x4x7
C)
2x4x3
D)
74x7–5x4x3
C
A
Simplify the expression by performing the indicated operations.
42)
8·4–550
42)
A)
16 –25 2
B)
8–25 2
C)
–21 2
D)
–2
Simplify the expression.
43)
4 3( 11 +3 )
43)
A)
433 +3
B)
411 +3
C)
12 11 +12
D)
433 +12
Find the square root.
44)
625
49
44)
A)
25
8
B)
25
7
C)
13
D)
26
7
45)
311 15 2
9 2
45)
A)
18 11
B)
24 33
C)
18 33
D)
24 2+ 3 11
46)
810
410 510
15 10
46)
A)
32 10
B)
27 10
C)
17 20
D)
32 20
47)
–481
47)
A)
4.264
B)
–3
C)
9
D)
Not a real number
B
48)
48k7q8
48)
A)
4k3q43
B)
4k3q43k
C)
4q43k7
D)
4k7q83k
B
49)
126
49)
A)
Irrational, 63.000
B)
Irrational, 11.225
C)
Not a real number
D)
Rational, 11.225
B
A
Solve the equation.
50)
m+ 3 =6
50)
A)
{33}
B)
{9}
C)
{81}
D)
51)
4256
625
51)
A)
4
5
B)
16
25
C)
64
125
D)
256
625
A
52)
5–243
52)
A)
–48.6
B)
3
C)
–3
D)
Not a real number
C
Perform the indicated operations. Assume that all variables represent nonnegative real numbers.
53)
3x +4108x+275x
53)
A)
7186x
B)
34 3x
C)
6186x
D)
35 3x
D
10
B
Simplify the expression.
54)
3 6
5
54)
A)
150
5
B)
3150
5
C)
3750
5
D)
330
5
55)
16
4
55)
A)
2
B)
24
C)
2 4
D)
4
Rationalize the denominator. Assume that all variables represent positive real numbers.
56)
14p3r
7m
56)
A)
2pmr
m
B)
p 2pmr
C)
p 2pmr
m
D)
p 2pmr
7m
Simplify and add or subtract wherever possible.
57)
1533+1233
57)
A)
2736
B)
2733
C)
–333
D)
2739
11
Find the product and simplify, if possible.
58)
621 ·8 9
58)
A)
48 3
B)
144
C)
321
D)
144 21
Simplify and add or subtract wherever possible.
59)
5+ 4 45 + 4 125
59)
A)
33 175
B)
8175
C)
8 5
D)
33 5
Find the perimeter of the figure.
60)
7 3
15 3
60)
A)
22 3
B)
44 3
C)
22 6
D)
44 6
Rationalize the denominator. Write the quotient in lowest terms.
61)
7
7 6 –7
61)
A)
42 – 1
41
B)
6+ 1
41
C)
42 + 1
43
D)
42 + 1
41
Find the length of the unknown side of a right triangle with legs a and b and hypotenuse c. Round to the nearest
thousandth, if necessary.
62)
a =10, b =24
62)
A)
c =22
B)
c =25
C)
c =26
D)
c =18
Identify the given number as “Rational”, “Irrational”, or “Not a real number”. If the number is rational, give its exact
value. If the number is irrational, give a decimal approximation to the nearest thousandth.
63)
–81
63)
A)
Irrational, –40.500
B)
Irrational, –9.000
C)
Rational, –9
D)
Not a real number
Find the square root. Express the answer as a whole number or as a square root. Do not use a calculator.
64)
(–2)2+32
64)
A)
10
B)
19
C)
13
D)
4
Solve the problem.
65)
The sum of 7 and the square root of some number is equal to 17. Find the number.
65)
A)
10
B)
20
C)
14
D)
100
Identify the given number as “Rational”, “Irrational”, or “Not a real number”. If the number is rational, give its exact
value. If the number is irrational, give a decimal approximation to the nearest thousandth.
66)
–138
66)
A)
Irrational, –11.747
B)
Not a real number
C)
Rational, –11.747
D)
Irrational, 11.747
Simplify the radical expression. Assume that all variables represent nonnegative real numbers.
67)
( 3x +y)2
67)
A)
3x +3xy +y
B)
3x + 2 3xy +y
C)
9x2+3xy +y2
D)
9x2+ 2 3xy +y2
68)
(5x + 10 7)2
68)
A)
25x2+4900
B)
25x2+700
C)
25x2+ 100x 7 +700
D)
25x2+ 100x 7 +4900
Simplify the radical.
69)
3216x4y5
69)
A)
6xy3xy2
B)
6xy3xy
C)
6xy2xy2
D)
5xy3xy2
Simplify the expression.
70)
8
5·40
70)
A)
8
B)
64
C)
40
D)
8
Perform the indicated operation and express the answer in simplest form.
71)
434–3634+536
71)
A)
4316 + 19 324 – 5 336
B)
4316 + 19 324 + 5 336
C)
4316 – 5 336
D)
4316 – 19 324 + 5 336
72)
1
19
72)
A)
19 19
B)
19
19
C)
1
19
D)
19
19
73)
3k12
8
73)
A)
k12
2
B)
k4
8
C)
k4
2
D)
k15
2
74)
5 9
b
74)
A)
414
B)
413
C)
213
D)
214
Solve the equation.
75)
q + 1 =3
75)
A)
{10}
B)
{8}
C)
{9}
D)
{16}
Perform the indicated operation and express the answer in simplest form.
76)
(7 +35)(7–35)
76)
A)
49 –325
B)
49 –35
C)
44
D)
24
Rationalize the denominator. Assume that all variables represent positive real numbers.
77)
64p7s2
11r
77)
A)
8ps 11pr
11r
B)
8p3s11pr
11r
C)
8ps 11p
11r
D)
8p3s11pr
r
Simplify the radical. Assume that all variables represent nonnegative real numbers.
78)
c18d10
78)
A)
c18d10
B)
c9d5
C)
c9d5
D)
c9d10
Solve the equation.
79)
2x + 5 –x – 2 = 3
79)
A)
{–2}
B)
{2, 38}
C)
{2}
D)
{3, 8}
Solve the problem.
80)
Fill in the blank.
7+711 cannot be simplified because the _________ are not the same.
80)
A)
radicands
B)
coefficients
C)
roots or indexes
D)
variables
Perform the indicated operations. Assume that all variables represent nonnegative real numbers.
81)
33125x+ 3 327x
81)
A)
83x
B)
24 3x
C)
33152x
D)
24x
Find the length of the unknown side of a right triangle with legs a and b and hypotenuse c. Round to the nearest
thousandth, if necessary.
82)
a =6, c =10
82)
A)
b =9
B)
b =7
C)
b =8
D)
b =10
83)
( 3 –9) ( m–3)
83)
A)
3m –9–9m + 3 3
B)
3m –9–3m + 3 3
C)
3m –9–9m +9
D)
3m +9–9m + 3 3
84)
8100
84)
A)
89, –89
B)
91, –91
C)
90, –90
D)
9, –9
Simplify the expression.
85)
11
64
85)
A)
11
64
B)
121
8
C)
11
8
D)
11
8
86)
–400
86)
A)
20
B)
200
C)
Not a real number
D)
–20
87)
41024
87)
A)
444
B)
16
C)
4416
D)
4
Write the quotient in lowest terms.
88)
30 –18 10
12
88)
A)
15 –9 5
6
B)
30 –6 5
2
C)
5–310
2
D)
10 –18 10
2
89)
The length of a rectangle is 120 meters, and the width is 27 meters. Find the measure of the
diagonal of the rectangle.
120 meters
27 meters
89)
A)
122 meters
B)
128 meters
C)
124 meters
D)
123 meters
90)
Fill in the blank.
4 3 +14 15 cannot be simplified because the _________ are not the same.
90)
A)
roots or indexes
B)
variables
C)
coefficients
D)
radicands
91)
9, –7 and 3, –15
91)
A)
14
B)
14
C)
10
D)
10
92)
3( 5 –7)
92)
A)
12 3
B)
15 –21
C)
3 5 +3 7
D)
36
Find the square root. Express the answer as a whole number or as a square root. Do not use a calculator.
93)
(–12)2+52
93)
A)
7
B)
11
C)
13
D)
17
Solve the problem.
94)
The year y when sales were s million dollars for a particular electronics company can be modeled
by the radical equation
y =1.3 s –3–6,
where y = 1 represents 2001, and so on.
Use the model to predict the sales for 2006 to the nearest tenth of a million.
94)
A)
$89.7 million
B)
$86.7 million
C)
$88.2 million
D)
$91.2 million
Solve the equation.
95)
36q –5=36q +5
95)
A)
{0}
B)
C)
{10}
D)
5
6
Simplify the radical expression. Assume that all variables represent nonnegative real numbers.
96)
( x –10)( 6–5)
96)
A)
6x –5x –415 +25 2
B)
6x –5x –215 +5 2
C)
x 6 – x 5–215 +5 2
D)
6x –5x –10 6+510
97)
8
5p
97)
A)
8 5p
B)
8 5p
5p
C)
64 5p
5p
D)
33p
98)
7·3
98)
A)
10
B)
21
C)
21
D)
7+ 3
99)
Two cars leave Springfield, Illinois at the same time. One travels north at 7 miles per hour and the
other travels west at 24 miles per hour. How far apart are they after 2 hours? (Hint: Use d = rt to
find the distance traveled by each car.)
7 mph
24 mph
99)
A)
55 miles
B)
47 miles
C)
60 miles
D)
50 miles
Solve the equation.
100)
x=5
100)
A)
{10}
B)
{25}
C)
{–25}
D)
{5}
Simplify.
101)
1
27 ·1
3
101)
A)
1
27
B)
27
3
C)
1
9
D)
1
327
102)
A(–7, –5)
B(–4, 1)
102)
A)
3 6
B)
3 5
C)
9 5
D)
9 6
Simplify.
103)
10
20 ·20
13
103)
A)
130
13
B)
10
13
C)
13 10
D)
10
13
104)
41
27
104)
A)
43
6
B)
343
C)
49
3
D)
43
3
105)
(2 –5 2)2
105)
A)
54 +20 2
B)
4–25 2
C)
54 –20 2
D)
4+25 2
106)
m10
n18 , n 0
106)
A)
m5
n18
B)
m5
n9
C)
m5
n9
D)
m10
n9
Perform the indicated operations. Assume that all variables represent nonnegative real numbers.
107)
7x2+ x 112
107)
A)
5x 7
B)
5 7
C)
4x 7
D)
x( 7+112)
108)
327y–3128y
108)
A)
33y–432y
B)
73y
C)
432y –33y
D)
3–432
A
D)
Rationalize the denominator. Write the quotient in lowest terms.
109)
5
8 –3
109)
A)
40 +5 3
–5
B)
40 +5 3
61
C)
5
8 – 5
3
D)
40 –5 3
61
B
D)
Simplify the expression by performing the indicated operations.
110)
531215 +3375·935
110)
A)
15375 +45315
B)
25375 +27375
C)
1539+4533
D)
30315 +9033
A
D)
Simplify the radical.
111)
66
111)
A)
233
B)
33 2
C)
433
D)
Cannot be simplified
D
D)
A
D)
Solve the equation.
112)
x= –8
112)
A)
{–64}
B)
{16}
C)
D)
{64}
Simplify the expression.
113)
316x4–83128x4
113)
A)
–30x32x
B)
–2x34x
C)
2x32x –8x34x
D)
2x32x –32x34x
114)
7·4
114)
A)
28
B)
14
C)
2 7
D)
2
115)
7 5 – 9 5
115)
A)
–210
B)
16 5
C)
–63 10
D)
–2 5
116)
x14
116)
A)
x7
B)
x6
C)
x7x
D)
x8
Rationalize the denominator. Assume that all variables represent positive real numbers.
117)
5x3y
13
117)
A)
513xy
13
B)
x65xy
13
C)
x265xy
13
D)
x65xy
13
Simplify the expression.
118)
364x4y5
118)
A)
4xy3xy2
B)
4xy2xy2
C)
4xy3xy
D)
2xy3xy2
A
Solve the equation.
119)
2k + 1 =19
119)
A)
{90}
B)
{–180}
C)
{360}
D)
{180}
D
Find the root.
120)
4–81
120)
A)
–3
B)
9
C)
3
D)
Not a real number
D
D
Solve the problem. Give the answer to the nearest thousandth if necessary.
121)
The diagram below shows the side view of a plan for a slanted roof. Find the unknown length in
this roof plan.
5 ft
8 ft
121)
A)
5.099 ft
B)
13 ft
C)
10.434 ft
D)
9.434 ft
Simplify the radical. Assume that all variables represent nonnegative real numbers.
122)
k6
49
122)
A)
k3
14
B)
k3
49
C)
k3
7
D)
k6
7
123)
529
123)
A)
25, –25
B)
24, –24
C)
46, –46
D)
23, –23
124)
3–49
124)
A)
–7
B)
–16.333
C)
–3.659
D)
–5.278
Find the square of the radical expression.
125)
19
16
125)
A)
–19
16
B)
19
16
C)
5
4
D)
45
32
126)
a =6, b =8
126)
A)
c =5
B)
c =7
C)
c =9
D)
c =10
127)
The velocity v of a meteorite approaching the earth is given by v =kd kilometers per second,
where d is the meteorite’s distance from the center of the earth and k is a constant. What is the
velocity of a meteorite that is 2000 kilometers away from the center of the earth, if k =150? Give
your answer as a simplified radical.
127)
A)
3000 5 kilometers per second
B)
3
40 kilometers per second
C)
3 5
2 kilometers per second
D)
15
2 5 kilometers per second
128)
8q – 7 =7
128)
A)
B)
21
4
C)
{7}
D)
{49}
129)
A rectangle has a length of 403 and a width of 83. What is the best estimate for its area?
129)
A)
180
B)
189
C)
210
D)
200
130)
33645m10
130)
A)
9m33m
B)
9m335
C)
9m335m
D)
45m3
131)
7
3+4
131)
A)
321 +3 7
12
B)
–21 –4 7
13
C)
–21 +4 7
13
D)
21 –4 7
7
Simplify and add or subtract wherever possible.
132)
1
4648+1
6162
132)
A)
9 2
B)
2
3162
C)
3 2
D)
6 2
133)
A rectangle has a length of 288 and a width of 77. What is the best estimate for its dimensions?
133)
A)
16 by 9
B)
17 by 8
C)
16 by 8
D)
17 by 9
Solve the equation.
134)
10 + x +11 – 5x = –1
134)
A)
{1}
B)
C)
{0}
D)
11
2
Solve the problem.
135)
Fill in the blank.
713 +813 =7+813 is an example of the ___________ property.
135)
A)
commutative
B)
distributive
C)
associative
D)
inverse
136)
A triangle has a base of 293 and a height of 260. What is the best estimate for its area?
136)
A)
136
B)
144.5
C)
2601
D)
144
Solve the equation.
137)
20x +20 = x + 6
137)
A)
{4, –4}
B)
{4}
C)
{4, 5}
D)
{–4}
Simplify the expression.
138)
49
16
138)
A)
1
B)
7
4
C)
7
4
D)
7
4
Solve the problem. Give the answer to the nearest thousandth if necessary.
139)
A boat travels 3 miles south and then 10 miles east. How far is the boat from its starting point?
South
3 mi East ––10 mi–->
139)
A)
5.22 mi
B)
10.44 mi
C)
6.5 mi
D)
54.5 mi
140)
–9
140)
A)
3
B)
–9
C)
–3
D)
9
Rationalize the denominator. Write the quotient in lowest terms.
141)
5+ 1
2+2
141)
A)
2 5 –10 +2–2
2
B)
2 5 +10 +2+2
2
C)
5–10 +2–2
2
D)
2 5 –10 +2–2
2+4 2
142)
x–5x –5= 1
142)
A)
–1
4
B)
1
4
C)
1
D)
9
4
Rationalize the denominator. Assume that all variables represent positive real numbers.
143)
7
32xy2
143)
A)
7 2x
8xy
B)
14xy
8xy
C)
14x
8xy
D)
14
8y x
D)
Find the root.
144)
3–64
144)
A)
8
B)
4
C)
–4
D)
Not a real number
C
D)
Simplify the expression.
145)
3500
145)
A)
20
B)
5320
C)
534
D)
5
C
D)
146)
12 c
6
146)
A)
36 6
B)
6 5
C)
36 5
D)
6 6
B
D)
C
Rationalize the denominator. Assume that all variables represent positive real numbers.
147)
50
x
147)
A)
52
x
B)
5x
x
C)
52x
D)
52x
x
148)
–8 3 – 8 12
148)
A)
–16 3
B)
–24 3
C)
–8 3
D)
24 3
Rationalize the denominator.
149)
35
9x2
149)
A)
3405x2
9x
B)
3405x
81
C)
315x
3x
D)
345x
9x
150)
29 2– 14 2
150)
A)
30
B)
15
C)
43 2
D)
15 2
Simplify the expression.
151)
81
28
151)
A)
9 7
7
B)
28
C)
9 7
14
D)
9 7
152)
Is 11 simplified?
152)
A)
Yes
B)
No
Write the quotient in lowest terms.
153)
54 +36 200
48
153)
A)
18 +36 200
8
B)
9+6200
8
C)
18 +120 2
24
D)
9+60 2
8
154)
–49
154)
A)
Not a real number
B)
7
C)
–24
D)
–7
Write the quotient in lowest terms.
155)
60 –108
90
155)
A)
60 –3
15
B)
10 –3
90
C)
10 –18
15
D)
10 –3
15
Solve the problem.
156)
A spherical ball has a volume of 288 inches. What is the radius of the ball? (V =4
3r3)
156)
A)
7 in.
B)
5 in.
C)
7in.
D)
6 in.
Rationalize the denominator. Write the quotient in lowest terms.
157)
x
6–x
157)
A)
6 x + x
36 – x
B)
6 x +6 x
36
C)
6 x – x
36 –x2
D)
–x+ x
36 – x
Perform the indicated operation and express the answer in simplest form.
158)
354+5556–255
158)
A)
3524 – 6 520 +530 – 2 525
B)
3524 + 6 520 +530 + 2 525
C)
3524 – 6 520 –530 – 2 525
D)
3524 – 2 525
Solve the problem.
159)
Fill in the blank.
8 2 +1032 cannot be simplified because the _________ are not the same.
159)
A)
coefficients
B)
radicands
C)
roots or indexes
D)
variables
Solve the equation.
160)
3k + 10 + 5 = 2k
160)
A)
B)
5
C)
5
3
D)
– 5
Simplify the radical.
161)
–108
161)
A)
–6 3
B)
–12 3
C)
–10
D)
–36
162)
2 3
162)
A)
120
B)
20 18
C)
80 6
D)
20 6
163)
342
163)
A)
14
B)
3.476
C)
6.481
D)
5.013
Simplify the radical.
164)
20
164)
A)
2 5
B)
5 2
C)
4
D)
10
Rationalize the denominator and simplify.
165)
–44
48
165)
A)
–11 48
12
B)
–11 3
3
C)
–11 3
12
D)
–33
3
Solve the equation.
166)
2x + 3 +4 – x = 4
166)
A)
B)
3, 11
9
C)
{3}
D)
{–3}
Find the product and simplify, if possible.
167)
3 2 ·9 4
167)
A)
54 2
B)
27 2
C)
18 2
D)
6 2
Provide an appropriate response.
168)
What is the smallest power to which both sides of the radical equation n4x + 2 =m1– 5x need be
raised so the radicals are eliminated whenever m and n are relatively prime, i.e. they have no
common integer divisor greater than 1?
168)
A)
m + n
B)
mn
C)
m + n
mn
D)
1
m+1
n
37
Simplify the expression.
169)
648x–327x–3x
169)
A)
14 3x
B)
221x
C)
14x 3
D)
3x 21
Solve the problem.
170)
A box in the shape of a cube has a volume of 27 cubic inches. What is the depth of the box? (V =s3)
170)
A)
6 in.
B)
5 in.
C)
3 in.
D)
9 in.
Simplify the radical.
171)
3 1
27
171)
A)
3
B)
1
3
C)
1
9
D)
1
33
Simplify and add or subtract wherever possible.
172)
20 + 5 245 – 6 125
172)
A)
–7 5
B)
52 5
C)
7 5
D)
–245 5
Simplify the expression by performing the indicated operations.
173)
8464 +4432 ·42
173)
A)
2444
B)
2448
C)
1644+12848
D)
1648+12844
38
Write the quotient in lowest terms.
174)
16 –24
24
174)
A)
8–6
12
B)
16 –6
12
C)
8–12
12
D)
8–6
24
Solve the equation.
175)
2x + 3 +4 – x = 4
175)
A)
{3}
B)
3, 11
9
C)
D)
{–3}
D)
176)
s =32 +4 s
176)
A)
{32}
B)
{128}
C)
{48}
D)
{64}
D)
Simplify the expression.
177)
(3 3 +8 5)(6 3 +9 5)
177)
A)
–306 +75 15
B)
18 3+72 5+75 15
C)
18 3+72 5
D)
414 +75 15
D)
Solve the problem.
178)
In electronics, the impedance Z of an alternating series circuit is given by the formula
Z =R2+X2, where R is the resistance and X is the reactance, both in ohms. Find the value of the
impedance Z if R =10 ohms and X =24 ohms.
178)
A)
26 ohms
B)
14 ohms
C)
22 ohms
D)
34 ohms
D)
D)
Find the square root. Express the answer as a whole number or as a square root. Do not use a calculator.
179)
242+452
179)
A)
38
B)
51
C)
21
D)
69
Perform the indicated operations and express the result in simplest form.
180)
(–6)2–4 (1)(–4)
180)
A)
417
B)
413
C)
217
D)
213
Solve the problem.
181)
Write an equivalent statement using the distributive property.
10313 +8313 =
181)
A)
10 +8326
B)
10 +8313
C)
80 313
D)
80 326
Solve the equation.
182)
2y +15 = y
182)
A)
B)
{5, –3}
C)
{2}
D)
{5
Rationalize the denominator and simplify.
183)
24
63
183)
A)
56
7
B)
8 7
21
C)
863
21
D)
8 7
7
Rationalize the denominator. Write the quotient in lowest terms.
184)
d
d+e
184)
A)
d–e
d–e
B)
d+e
d–e
C)
d+de
d+e
D)
d–de
d–e
185)
–400
49
185)
A)
–25
3
B)
20
7
C)
Not a real number
D)
–20
7
Solve the equation.
186)
35a – 7 =32a + 9
186)
A)
3
16
B)
2
3
C)
16
7
D)
16
3
Solve the problem.
187)
Write an equivalent statement using the distributive property.
5 2 +14 2=
187)
A)
70 4
B)
70 2
C)
5+14 4
D)
5+14 2
Rationalize the denominator. Write the quotient in lowest terms.
188)
5
k–5
188)
A)
5( k –5)
k +25
B)
5( k +5)
k –5
C)
5( k +5)
k –25
D)
5( k +5)
k +5
189)
The radius of the circular top or bottom of a tin can with a surface area S and a height h is given by
r =–h +h2+ .64S
2.
What radius should be used to make a can with a height of 15 inches and a surface area of 625
square inches?
189)
A)
8 inches
B)
20 inches
C)
7 inches
D)
5 inches
Simplify the expression.
190)
( 7 +5)( 7–5)
190)
A)
32
B)
7– 2 5
C)
2
D)
–18
Simplify and add or subtract wherever possible.
191)
418 + 4 32
191)
A)
4 2
B)
–28 2
C)
28 2
D)
–4 2
42
Simplify the expression.
192)
60 30
10 6
192)
A)
6 5
B)
10 5
C)
30
D)
6 6
Simplify the radical.
193)
3x22
193)
A)
x73x
B)
x73x2
C)
x143x2
D)
x143x
Simplify the expression.
194)
499 +44
194)
A)
511
B)
14 11
C)
40 11
D)
44 3+11 2
Find the product and simplify, if possible.
195)
7·7
195)
A)
7
B)
14
C)
49
D)
7
196)
A car dealer advertised a big sale by stretching a string of banners from the top of the building to
the edge of the driveway. If the building is 16 m high and the driveway is 48 m from the building,
how long is the string of banners?
196)
A)
8.0 m
B)
50.6 m
C)
45.3 m
D)
22.6 m
Find the product and simplify, if possible.
197)
3·21
197)
A)
63
B)
3 7
C)
7
D)
9 7
Solve the equation.
198)
3x + 10 = 5 – 2x
198)
A)
5
4, 9
B)
3
4
C)
3
4, 5
D)
{5}
Rationalize the denominator and simplify.
199)
64
5
199)
A)
33
B)
8 5
C)
8 5
5
D)
64 5
5
Solve the equation.
200)
2k + 1 + 22 =17
200)
A)
{72}
B)
C)
{288}
D)
{–144}
Find the square root. Express the answer as a whole number or as a square root. Do not use a calculator.
201)
202+482
201)
A)
44
B)
68
C)
52
D)
28
44
Use a calculator with a cube root key to find the root. Round to the nearest thousandth.
202)
3–127.5
202)
A)
–5.033
B)
–42.5
C)
–11.292
D)
–7.259
203)
632–43128
203)
A)
632–43128
B)
–1032
C)
232
D)
1032
Simplify.
204)
11
5·11
25
204)
A)
11
25 5
B)
11 5
25
C)
5
25 11
D)
11 5
5
Simplify and add or subtract wherever possible.
205)
–275 – 4 48 + 10 243
205)
A)
–214 3
B)
64 3
C)
–2 3
D)
214 3
45
Simplify and add or subtract wherever possible.
Rationalize the denominator.
206)
3 4
5
206)
A)
100
5
B)
320
5
C)
3500
5
D)
3100
5
207)
Find the perimeter of a lot with sides measuring 2 8, 550, 532, and 475 yards.
207)
A)
98 + 20 3 yd
B)
49 + 20 3 yd
C)
49 2+ 20 3 yd
D)
69 2 yd
Solve the equation.
208)
35y – 7 =33y – 5
208)
A)
– 1
B)
–5
8
C)
1
D)
–12
5
Simplify the radical.
209)
364k9
209)
A)
4k12
B)
64k3
C)
4k9
D)
4k3
Solve the equation.
210)
x2– 5x +7= x –3
210)
A)
{16}
B)
C)
16
5
D)
{2}
Solve the problem.
211)
The time T in seconds for a pendulum of length L feet to make one swing is given by T = 2L
37.
How long is a pendulum (to nearest hundredth) if it makes one swing in 2 seconds? Use 3.14 for .
211)
A)
3.75
B)
37
C)
23.57
D)
148
212)
Which one of the following would be an appropriate choice for multiplying the numerator and the
denominator of 32
35 in order to rationalize the denominator?
212)
A)
35
B)
33
C)
325
D)
32
Solve the equation.
213)
16 –3y =4–y
213)
A)
{4, 8}
B)
{4, –4}
C)
{0, –4}
D)
{0, 4}
Rationalize the denominator and simplify.
214)
77
214)
A)
1
B)
7 7
C)
7
D)
7
Rationalize the denominator. Write the quotient in lowest terms.
215)
3– 3
2+ 9
215)
A)
6– 27 – 3 2+ 9 3
83
B)
6+ 27 – 3 2– 9 3
83
C)
6– 27 – 3 2+ 9 3
–79
D)
–6– 27 + 3 2+ 9 3
79
216)
x –3=2x – 3
216)
A)
{3}
B)
C)
{6, 2}
D)
{6}
Simplify the expression.
217)
(3 +5)2
217)
A)
14 +6 5
B)
14 +3 5
C)
8+6 5
D)
9+6 5
48
Find the square of the radical expression.
218)
9
218)
A)
9
2
B)
9
C)
6
D)
3
Rationalize the denominator and simplify.
219)
36 14
30 5
219)
A)
670
25
B)
614
5
C)
670
5
D)
614
25
Solve the equation.
220)
3x – 2 +11 + x = –1
220)
A)
{5}
B)
–5
C)
D)
{0}
Simplify the radical.
221)
3–27a8b5
221)
A)
–3a2b3a2b2
B)
3ab3a3b3
C)
3ab3a2b2
D)
3 a2b2
Find the root.
222)
4–1296
222)
A)
–6
B)
36
C)
6
D)
Not a real number
Rationalize the denominator. Assume that all variables represent positive real numbers.
223)
25p3
r
223)
A)
5p2p
r
B)
5p2pr
r
C)
5p pr
r
D)
5p p
r
C
224)
6·22
224)
A)
66
B)
233
C)
433
D)
132
B
Solve the equation.
225)
2 x =9x +6
225)
A)
6
11
B)
6
13
C)
–6
7
D)
–6
5
D
Find the square root. Express the answer as a whole number or as a square root. Do not use a calculator.
226)
92+122
226)
A)
8
B)
15
C)
21
D)
3
B
50
D
Rationalize the denominator. Assume that all variables represent positive real numbers.
227)
4a
5
227)
A)
29
B)
4a 5
C)
4a 5
5
D)
16a 5
5
Simplify.
228)
1
14 ·14
3
228)
A)
14 3
3
B)
3
C)
3
3
D)
1
3
229)
Below is a diagram of a water slide. The slide is 25 ft long. The ladder leading to the slide is 18 ft
long. How far is it from the end of the slide to the foot of the ladder?
18 ft 25 ft
?
229)
A)
21.5 ft
B)
17.349 ft
C)
8.675 ft
D)
150.5 ft
Simplify the radical.
230)
364
27
230)
A)
64
27
B)
16
9
C)
4
27
D)
4
3
Simplify.
231)
2
5·5
2
231)
A)
1
B)
100
10
C)
10
D)
0
Rationalize the denominator.
232)
50
x
232)
A)
5x
x
B)
52x
C)
52
x
D)
52x
x
D
Simplify.
233)
1
14 ·1
22
233)
A)
308
308
B)
77
77
C)
77
154
D)
77
308
C
234)
95m11p7– 2m2p 5mp2
234)
A)
7m2p 5mp2
B)
7
C)
11m2p 5mp2
D)
Cannot simplify
A
A
Solve the problem.
235)
The product of 2 and the square root of some number is equal to that number decreased by 8. Find
the number.
235)
A)
12
B)
8
C)
32
D)
16
236)
Find the measure of the unknown leg of this right triangle. Give its length in simplified radical
form, and give a decimal approximation to the nearest thousandth.
15 feet
4 feet
236)
A)
241; 15.524
B)
434; 20.833
C)
466; 21.587
D)
209; 14.457
Perform the indicated operations and express the result in simplest form.
237)
(7 – 4)2+(4 – 8)2
237)
A)
25
B)
317
C)
153
D)
5
Rationalize the denominator and simplify.
238)
–6
5
238)
A)
–6 5
5
B)
–6
5
C)
–30
6
D)
–30
5
Rationalize the denominator.
239)
5
8 –3
239)
A)
40 +5 3
61
B)
40 +5 3
–5
C)
5
8 – 5
3
D)
40 –5 3
61
240)
49
240)
A)
14, –14
B)
8, –8
C)
9, –9
D)
7, –7
Simplify the expression.
241)
( 3 +10) ( 10 +6)
241)
A)
413
B)
30 +215
C)
30 +3 2 +10 +215
D)
30 +3 2 +100+215
Solve the problem.
242)
On a sunny day, a flag pole and its shadow form the sides of a right triangle. If the hypotenuse is 40
m long and the shadow is 32 m, how tall is the flag pole?
242)
A)
24 m
B)
51 m
C)
72 m
D)
64 m
243)
138
243)
A)
Rational, 69.000
B)
Irrational, 11.747
C)
Rational, 11.747
D)
Irrational, 69.000
244)
720
244)
A)
14 5
B)
20 7
C)
31
D)
140
Solve the equation.
245)
41 – 2x + 3 =9 – 2x + 7
245)
A)
7
2
B)
C)
5
2
D)
55
2
Simplify the expression.
246)
8
125 ·2
5
246)
A)
4
25
B)
25
C)
2
5
D)
2
5
Find the distance between the pair of points.
247)
0, –10 and 4, –6
247)
A)
32
B)
8
C)
32
D)
8
Solve the equation.
248)
32x2+8x +5=3x
248)
A)
–1, –5
2
B)
–5
2, 0
C)
–2
5, 0
D)
–1, –2
5
Simplify.
249)
2
9·1
3
249)
A)
2
9
B)
6
9
C)
54
27
D)
1
32
3
Simplify the radical.
250)
3x20
250)
A)
x63x2
B)
x123x
C)
x63x
D)
x123x2
251)
49
251)
A)
7
B)
Not a real number
C)
24
D)
8
252)
180x2
252)
A)
6 5x
B)
5x26
C)
180x
D)
6x 5
Rationalize the denominator.
253)
–35
349
253)
A)
–7349
B)
–5349
C)
–3537
D)
–537
254)
If an investment of P dollars grows to A dollars in two years, the annual rate of return on the
investment is given by
r =A–P
P. Jared Spencer bought a collector’s coin set for $290 and sold it two years later for
$525. What was the approximate annual rate of return of his investment? Round to the nearest
tenth of a percent.
254)
A)
9.0%
B)
29.6%
C)
40.5%
D)
34.6%
255)
715
11 15
255)
A)
36 30
B)
36 15
C)
18 15
D)
18 30
Perform the indicated operations and express the result in simplest form.
256)
(–4–5)2+(3 –9)2
256)
A)
313
B)
87
C)
5 3
D)
37
57
Find the root.
257)
3343
257)
A)
18
B)
49
C)
7
D)
Not a real number
258)
–529
441
258)
A)
23
21
B)
Not a real number
C)
–23
21
D)
–6
5
C
Rationalize the denominator. Write the quotient in lowest terms.
259)
5– 3
2+ 7
259)
A)
10 + 21 – 3 2– 7 5
–47
B)
10 – 21 – 3 2+ 7 5
51
C)
10 – 21 – 3 2+ 7 5
–47
D)
10 + 21 – 3 2– 7 5
51
A
Simplify the expression.
260)
(10 +5)( 10 –5)
260)
A)
10 – 2 50
B)
5
C)
10 –10 10
D)
15
B
58
C
261)
81
261)
A)
Rational, 9
B)
Not a real number
C)
Irrational, 40.500
D)
Rational, 40.500
262)
a =3, b =7
262)
A)
c =10
B)
c =4.472
C)
c =7.616
D)
c =21
263)
4q – 9 =5
263)
A)
4
B)
17
2
C)
– 1
D)
7
2
Rationalize the denominator and simplify.
264)
30
6
264)
A)
5
B)
5
6
C)
5
5
D)
30
6
Find all square roots of the number.
265)
25
361
265)
A)
1
4, –1
4
B)
6
19, –6
19
C)
5
19, –5
19
D)
1
15, –1
15
266)
–3 6x
y
266)
A)
–36xy2
y
B)
–36x2y
y
C)
–36x2y2
y
D)
–36xy
y
Solve the equation.
267)
2x + 15 – x = 6
267)
A)
{–7, –3}
B)
{–3}
C)
D)
{–7}
Rationalize the denominator and simplify.
268)
9
5
268)
A)
34
B)
81 5
5
C)
9 5
5
D)
9 5
Find the distance between the pair of points.
269)
–1
2, 8
9 and 1
2, –1
9
269)
A)
1
B)
3
C)
2
D)
2
Simplify the expression.
270)
(12 +4)( 12 –4)
270)
A)
28
B)
–4
C)
8
D)
12 – 2 4
271)
16
81
271)
A)
4
9
B)
4
9
C)
0
D)
4
9
Simplify the radical expression. Assume that all variables represent nonnegative real numbers.
272)
(5 t +7)(6 t –21)
272)
A)
30 t+6 7t –521t–7 3
B)
30t +6 7t +521t+7 3
C)
30 t+6 7t +521t+7 3
D)
30t +6 7t –521t–7 3
61
Rationalize the denominator.
273)
5
3y
273)
A)
53y2
B)
5y
C)
53y
y
D)
53y2
y
274)
–132
274)
A)
Irrational, –11.489
B)
Irrational, 11.489
C)
Rational, –11.489
D)
Not a real number
Perform the indicated operations and express the result in simplest form.
275)
(3 – (–2))2+(–7–5)2
275)
A)
13
B)
145
C)
15
D)
15
Simplify the radical. Assume that all variables represent nonnegative real numbers.
276)
36m13n6
276)
A)
6m5n3m
B)
6m6n3m
C)
6m7n4
D)
6m6n3
Simplify the expression.
277)
(3 –2)(4 5 +9)
277)
A)
12 5+27 –410 –9 2
B)
12 5–27 –410 –2
C)
12 5+27 –10 +9 2
D)
12 5+27 –20 2–910
Solve the problem. Give the answer to the nearest thousandth if necessary.
278)
A painter leans a ladder against one wall of a house (as shown below). The ladder is 26 ft long. The
base of the ladder is 20 ft from the house. How high is the wall?
?26 ft
20 ft
278)
A)
23 ft
B)
138 ft
C)
8.307 ft
D)
16.613 ft
279)
A(–7, 5)
B(–3, –1)
279)
A)
413
B)
213
C)
226
D)
426
Solve the equation.
280)
4x2+120x=5
280)
A)
{–25, 5}
B)
{–5, 25}
C)
{–125, 5}
D)
{–5, 125}
Simplify the radical expression. Assume that all variables represent nonnegative real numbers.
281)
( 7x – 7)( 3x + 6)
281)
A)
x21 – 42
B)
x 3 – 42
C)
x21 +3x – 42
D)
x21 + 6 7x – 7 3x – 42
Solve the equation.
282)
8x + 1 – 1 = x
282)
A)
{0, 7}
B)
{0}
C)
{7}
D)
{0, 6}
283)
x + 6 +2 – x = 4
283)
A)
{–2}
B)
{0}
C)
{2, –2}
D)
{31, –2}
284)
x + 7 + 5 = x
284)
A)
{2, 9}
B)
{2}
C)
{9, 18}
D)
{9}
64
Rationalize the denominator.
285)
33
36
285)
A)
18
B)
318
6
C)
3108
6
D)
3648
6
Simplify the expression.
286)
( 2 +5)2
286)
A)
7+ 2 10
B)
14 + 2 10
C)
7+10
D)
29 + 2 10
Solve the problem.
287)
A cube–shaped box must be constructed to contain 108ft3. What should the side length of the box
be? Give your answer in exact form.
287)
A)
3 4 ft
B)
334 ft
C)
3312 ft
D)
3 ft
Find the square root. Express the answer as a whole number or as a square root. Do not use a calculator.
288)
62+82
288)
A)
10
B)
2
C)
14
D)
5
65
Find the distance between the pair of points.
289)
3
2, 13
6 and –1
2, 1
6
289)
A)
8
B)
8
C)
5
D)
2
Solve the problem.
290)
Suppose that there is no straight path for driving between towns A and B. To drive from Town A to
Town B, it is necessary to travel due east for 21 miles, then due north for 18 miles. How far apart, to
the nearest tenth of a mile, are the towns?
290)
A)
6.2 mi
B)
345.0 mi
C)
27.7 mi
D)
459.0 mi
291)
A rectangular coal bin has a length of 27 feet and a width of 75 feet. What is its perimeter?
291)
A)
16 5 ft
B)
8 5 ft
C)
16 3 ft
D)
8 3 ft
292)
a =20, c =52
292)
A)
b =49
B)
b =36
C)
b =56
D)
b =48
Simplify the radical.
293)
3–1
125
293)
A)
–1
10
B)
–1
5
C)
1
5
D)
–5
Solve the problem. Give the answer to the nearest thousandth if necessary.
294)
A long–distance runner runs 5 miles south and then 9 miles east. How far is the runner from the
starting point?
South
5 mi East ––9 mi–>
294)
A)
5.292 mi
B)
14 mi
C)
11.296 mi
D)
10.296 mi
Simplify the radical.
295)
56
295)
A)
28
B)
7
C)
14 2
D)
214
Solve the problem. Give the answer to the nearest thousandth if necessary.
296)
The diagram below shows a rope connecting the top of a pole to the ground. The rope is 16 yd long
and touches the ground 13 yd from the pole. How tall is the pole?
?16 yd
13 yd
296)
A)
14.5 yd
B)
9.327 yd
C)
43.5 yd
D)
4.664 yd
Perform the indicated operation and express the answer in simplest form.
297)
35 (7 35–325)
297)
A)
6325
B)
735–5
C)
735–535
D)
7325 –5
Solve the equation.
298)
5a – 4 =2a + 9
298)
A)
13
7
B)
5
3
C)
3
13
D)
13
3
299)
s =128 +8 s
299)
A)
{192}
B)
{256}
C)
{128}
D)
{512}
Find the distance between the pair of points.
300)
–1
2, 17
9 and 5
2, –1
9
300)
A)
12
B)
13
C)
13
D)
14
Solve the equation.
301)
5y – 3 =3y – 1
301)
A)
– 1
B)
–4
5
C)
–1
8
D)
1
302)
38
302)
A)
19
B)
6.2
C)
38
D)
76
303)
–49
303)
A)
Irrational, –24.500
B)
Not a real number
C)
Rational, –7
D)
Irrational, –7.000
304)
6·3– 4 50
304)
A)
–2 2
B)
9– 20 2
C)
–17 2
D)
6– 20 2
305)
336(36–8 )
305)
A)
3216 –8336
B)
6–8336
C)
636–8
D)
636–48
306)
36m19
306)
A)
6m8m
B)
6m9m
C)
6m10
D)
6m9
307)
1936
307)
A)
46, –46
B)
88, –88
C)
44, –44
D)
45, –45
Simplify the radical expression. Assume that all variables represent nonnegative real numbers.
308)
( 6 +z)( 6–z)
308)
A)
6z
B)
6– z
C)
6– 2 6z
D)
6– 2 z
Find the square of the radical expression.
309)
25x2+4
309)
A)
25x +2
B)
25x +4
C)
25x2+4
D)
5x +2
Perform the indicated operation and express the answer in simplest form.
310)
(39+4)(33–5)
310)
A)
–13 –5·39
B)
–17 –539+433
C)
–17
D)
–32 +17 ·33
Simplify the radical expression. Assume that all variables represent nonnegative real numbers.
311)
( x –9y)2
311)
A)
x– 2 9xy +9y
B)
x2–9xy +y2
C)
x–9xy +y
D)
x2– 2 9xy +y2
Solve the equation.
312)
2x + 3 –x + 1 = 1
312)
A)
B)
{3, –1}
C)
{3}
D)
{–3, –1}
70
Rationalize the denominator. Assume that all variables represent positive real numbers.
313)
25p7
r
313)
A)
5 p7r
r
B)
5p p
r
C)
5p3p
r
D)
5p3pr
r
Solve the problem.
314)
A building has a ramp to its front doors to accommodate the handicapped. If the distance from the
building to the end of the ramp is 18 feet and the height from the ground to the front doors is 5 feet,
how long is the ramp?
314)
A)
7.1 ft
B)
4.8 ft
C)
18.7 ft
D)
17.3 ft
Rationalize the denominator. Write the quotient in lowest terms.
315)
6–5
6+5
315)
A)
31 – 12 5
41
B)
41 + 12 5
31
C)
41 – 12 5
31
D)
1
Solve the problem.
316)
The distance d in miles that can be seen on the surface of the ocean is given by d =1.5 h, where h
is the height in feet above the surface. How high (to the nearest foot) would a platform have to be to
see a distance of 16.5 miles?
316)
A)
408
B)
272
C)
110
D)
121
Simplify the radical.
317)
3384
317)
A)
24
B)
4324
C)
4
D)
436
Find the root.
318)
481
318)
A)
4.264
B)
9
C)
3
D)
Not a real number
C
319)
A(3, –1)
B(1, 7)
319)
A)
60
B)
217
C)
60 15
D)
10
B
D
Simplify the expression.
320)
44 48
11 8
320)
A)
4 6
B)
4 8
C)
24
D)
11 6
321)
Is (–2)(–8) = 4?
321)
A)
Yes
B)
No
322)
Find the perimeter of a triangle with sides measuring 480, 280, and 4 8 meters.
322)
A)
32 5 m
B)
24 5+ 8 2 m
C)
24 + 8 2 m
D)
24 5+ 8 m
323)
32x2y
323)
A)
4xy 2
B)
4xy22
C)
4x22 y
D)
4 x 2 y
Simplify the expression.
324)
35 6
5 3
324)
A)
7 2
B)
5 2
C)
14
D)
7 3
Find the square root. Express the answer as a whole number or as a square root. Do not use a calculator.
325)
12+52
325)
A)
5
B)
31
C)
6
D)
26
Find the product and simplify, if possible.
326)
15 ·48
326)
A)
12 5
B)
–12 5
C)
20 3
D)
–20 3
Rationalize the denominator and simplify.
327)
9
20
327)
A)
3 5
10
B)
20
C)
3 5
5
D)
3 5
Simplify.
328)
9
32 ·1
16
328)
A)
3 2
2
B)
34
C)
3 2
32
D)
3 2
8
Solve the equation.
329)
p2– 4p + 36 = p + 2
329)
A)
– 2
B)
{4}
C)
{–4}
D)
{6}
74
330)
x + 3 = x – 3
330)
A)
{1, 13}
B)
{6}
C)
{1, 6}
D)
{6, 13}
Use a calculator with a cube root key to find the root. Round to the nearest thousandth.
331)
3225
331)
A)
15
B)
75
C)
6.082
D)
8.772
332)
98 ·72
332)
A)
72
B)
42 2
C)
42
D)
84
333)
3 7
3 7
333)
A)
6 7
B)
12 28
C)
614
D)
12 7
Solve the problem.
334)
In a manufacturing process, three quantities p, r, and s are related by the equation p =r
s. Find p
when r = 11 and s = 288. Give your answer as a simplified radical.
334)
A)
22
12
B)
211
24
C)
22
24
D)
11 2
24
335)
b =19, c =22
335)
A)
a =29.069
B)
a =10.63
C)
a =11.091
D)
a =465
Solve the equation.
336)
7q –6=7q +6
336)
A)
B)
6
7
C)
{0}
D)
{12}
Simplify the expression.
337)
6 2 –575
337)
A)
–3 3
B)
–23 3
C)
4–25 3
D)
6–25 3
Find the root.
338)
5243
338)
A)
3
B)
48.6
C)
4
D)
Not a real number
Solve the equation.
339)
x –5=4x – 15
339)
A)
{10}
B)
{5}
C)
D)
{4}
A
Simplify the radical.
340)
3–27
64
340)
A)
–3
4
B)
3
4
C)
9
16
D)
–27
64
A
341)
680x2–245x2–5x2
341)
A)
17x 5
B)
4x 35
C)
18x 5
D)
3x 35
A
Simplify the radical.
342)
3m12
342)
A)
m5
B)
m4m
C)
m4
D)
m312
C
A
Rationalize the denominator.
343)
39p
316q
343)
A)
336pq2
4q
B)
336pq
4q
C)
9pq
4q
D)
39pq2
4q
Find the square root. Express the answer as a whole number or as a square root. Do not use a calculator.
344)
(–18)2+242
344)
A)
30
B)
16
C)
42
D)
Perform the indicated operations. Assume that all variables represent nonnegative real numbers.
345)
35x6y– 2x 5xy
345)
A)
35xy – 2x 5xy
B)
2x 5xy
C)
x5xy
D)
Cannot simplify
346)
The radius of the circular top or bottom of a tin can with a surface area S and a height h is given by
r =–h +h2+ .64S
2.
What radius should be used to make a can with a height of 15 inches and a surface area of 2025
square inches?
346)
A)
12 inches
B)
7 inches
C)
27 inches
D)
14 inches
347)
On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 35 m
long and the tree is 28 m tall, how long is the shadow?
347)
A)
63 m
B)
49 m
C)
45 m
D)
21 m
348)
28 ·x, x 0
348)
A)
2 7x
B)
14x
C)
5 x
D)
7 2x
349)
Is 25 =5 ?
349)
A)
No
B)
Yes
350)
x9
350)
A)
x4
B)
x5
C)
x4x
D)
x3x
351)
If an investment of P dollars grows to A dollars in two years, the annual rate of return on the
investment is given by
r =A–P
P. Angela Ramos invested $780 in a money market fund. Two years later, her
investment was worth $1211. Find the approximate annual rate of return on her investment.
Round to the nearest tenth of a percent.
351)
A)
7.4%
B)
19.6%
C)
24.6%
D)
27.6%
Solve the equation.
352)
k+ 8 =7
352)
A)
B)
{225}
C)
{–1}
D)
{1}
Simplify the expression.
353)
( 5 – 3)( 7– 5)
353)
A)
–735 + 15
B)
35 – 5 5– 3 7+ 15
C)
35 – 8 7+ 15
D)
35 + 15
Write the quotient in lowest terms.
354)
13 10 – 39
13
354)
A)
–2
B)
10 + 3
C)
10 – 3
D)
13 10 – 3
Rationalize the denominator.
355)
511
2
355)
A)
522
2
B)
10 22
C)
522
D)
522
4
Solve the equation.
356)
17x –20 =4 x
356)
A)
{4}
B)
{8}
C)
{1}
D)
{20}
Answer Key
Testname: C8
Answer Key
Testname: C8
Answer Key
Testname: C8
Answer Key
Testname: C8
Answer Key
Testname: C8
Answer Key
Testname: C8
Answer Key
Testname: C8
Answer Key
Testname: C8