Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1)
If a > 0, which of the following correctly describes –-a ?
1)
A)
Positive
B)
Not real
C)
Zero
D)
Negative
2)
If n is even, under what condition is na negative?
2)
A)
When a is positive
B)
When a is negative
C)
When a is zero
D)
Never
3)
If a < 0, which of the following correctly describes –-a ?
3)
A)
Not real
B)
Positive
C)
Negative
D)
Zero
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
4)
Explain why if n is odd, x1/n is defined even if x is negative.
4)
5)
If A = x +y, and B is the conjugate of A, then what is the product AB?
5)
6)
If n is a positive integer, does nxn= x? Explain.
6)
7)
What is wrong with this? (9x3)-1 =9x-3
7)
Explain the mistake, then simplify correctly.
8)
x=-4
( x )2=(-4)2
x =16
8)
Rationalize the equation, then use it to solve the problem.
9)
Police use a formula s = S l
L, where S is the test–car speed and L is the test–skid length,
to find the actual speed s in an accident which left a skid mark of l. Find the speed (nearest
tenth) when S = 54 mph, l = 150 ft, L = 100 ft.
9)
Explain the mistake, then simplify correctly.
10)
40
10 =4
1
11)
x + 4=7
(x + 4 )2=72
x +16 =49
x +16 –16 =49 –16
x =33
Provide an appropriate response.
12)
Explain why the sum 4625–5243–4625 can be simplified quickly.
13)
How many real number cube roots does any negative number have?
Explain the mistake, then simplify correctly.
14)
20
5=4
Provide an appropriate response.
15)
Tell whether the statement is true or false. Explain.
According to the quotient rule for radicals, na
nb=na
b, where b 0.
16)
Can a represent a negative real number?
Explain the mistake, then simplify correctly.
17)
3
11 =3
11 ·11
11 =11 3
11
Provide an appropriate response.
18)
Explain why the following expression cannot be simplified further:
13 a–11 a
19)
Choose values for n, a, and b to demonstrate the truth or falsity of the statement:
na+nb=na + b.
Rationalize the equation, then use it to solve the problem.
20)
The time T in seconds required for a pendulum of length L feet to make one swing is given
by T = 2L
32. How long is a pendulum (to nearest hundredth of a foot) if it makes one
swing in 3 seconds? Use 3.14 for .
Provide an appropriate response.
21)
Explain how to evaluate (-125)2/3.
2
22)
Tell whether the statement is true or false. If it is false, give the correct answer. Explain.
3x · 3x = x
23)
Explain why 3-13 and –313 represent the same number.
24)
How many real square roots does any positive number have?
25)
Tell whether the statement is true or false. If it is false, give the correct answer. Explain.
4x · 4x = x
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the root. Assume that variables represent nonnegative values.
26)
57776t25
26)
A)
6t5
B)
7t10
C)
7t5
D)
6t10
Write the following as a single radical. Assume that all variables represent nonnegative values.
27)
47m
27)
A)
28 m11
B)
28 m
C)
7m4
D)
11 m
Rationalize the denominator. Assume variables represent non–negative values.
28)
21
22
28)
A)
505
B)
21 22
22
C)
441 22
22
D)
21 22
Use the rules of exponents to simplify. Write the answer with positive exponents. Assume that all variables represent
positive values.
29)
(9a1/7b5/7)2
29)
A)
18a2/7b5/7
B)
9a2/7b10/7
C)
81a2/7b10/7
D)
81(ab)10/7
Solve the problem.
30)
The radius, r, of a sphere can be found using the formula r = S
4, where S is the surface area. If the
surface area is 15,483 square inches, what is the radius? (Use 3.14 for , and round your answer to
the nearest tenth of an inch.)
30)
A)
62.2 in.
B)
35.1 in.
C)
110.2 in.
D)
70.2 in.
31)
The radius, r, of a right circular cone can be found using the formula r = 3V
h, where V is the
volume and h is the height. If the volume is 519 cubic inches and the height is 18 inches, what is the
radius? (Use 3.14 for , and round your answer to the nearest tenth of an inch.)
31)
A)
5.2 in.
B)
3.0 in.
C)
2.6 in.
D)
5.5 in.
3
Find the root. Assume that variables represent nonnegative values.
32)
169x10y16
32)
A)
13x10y16
B)
13x5y8
C)
14x5y8
D)
12x5y8
Find the root. Assume that variables represent any real number.
33)
30.008(x + 8)3
33)
A)
0.2(x + 2)3
B)
0.2(x + 8)
C)
0.2(x + 2)
D)
0.4(x + 8)
Use a calculator to approximate the root to the nearest thousandth.
34)
5–78
34)
A)
-2.420
B)
-2.402
C)
-2.411
D)
-2.390
Write the following in exponential form. Assume that all variables represent positive values.
35)
18
5y2
35)
A)
18y-5/2
B)
18y-2/5
C)
18y2/5
D)
18y5/2
Find the product and write the answer in simplest form. Assume variables represent nonnegative values.
36)
15 ·48
36)
A)
20 3
B)
20 5
C)
12 5
D)
12 3
37)
2
r·s
5
37)
A)
rs
10
B)
2s
10rs
C)
10rs
5r
D)
2s
5r
Multiply.
38)
(9 – 3i)(2+ 9i)
38)
A)
45 – 75i
B)
-9 – 87i
C)
-27i2+ 75i + 18
D)
45 + 75i
Find the product and write the answer in simplest form. Assume variables represent nonnegative values.
39)
3xy5·3x19y20
39)
A)
x6y73x2y2
B)
x6y83x2y
C)
x6y93xy
D)
x6y83xy2
Multiply.
40)
(6 – 5i)(4+ 7i)
40)
A)
59 – 22i
B)
-11 – 62i
C)
-35i2+ 22i + 24
D)
59 + 22i
Use a calculator to approximate the root to the nearest thousandth.
41)
6128
41)
A)
2.245
B)
2.224
C)
2.215
D)
2.233
4
Rationalize the denominator and simplify. Assume that variables represent positive values.
42)
3
3 2 – 3
42)
A)
1
7( 6 + 1)
B)
1
5( 2 + 1)
C)
1
5( 6 – 1)
D)
1
5( 6 + 1)
Find the root. Assume that variables represent any real number.
43)
81x2
43)
A)
9x
B)
9 x
C)
81x
D)
–9 x
Write the following in exponential form. Assume that all variables represent positive values.
44)
85
44)
A)
1
58
B)
81/5
C)
51/8
D)
–51/8
Solve.
45)
3x – 2 +11 + x = –1
45)
A)
5
B)
–5
2
C)
0
D)
No solution
Use a calculator to approximate the root to the nearest thousandth.
46)
–2336
46)
A)
–48.332
B)
–48.337
C)
–2336.000
D)
–48.329
Rationalize the numerator. Assume that variables represent positive values.
47)
5x – 3
6
47)
A)
5x – 3
6( 5x – 3)
B)
5x – 3
6( 5x + 3)
C)
5x – 9
6( 5x – 3)
D)
5x – 9
6( 5x + 3)
Evaluate the root, if possible.
48)
–529
25
48)
A)
–22
B)
–23
5
C)
Not real
D)
23
5
Rewrite the following using radicals; then simplify if possible.
49)
25-1/2
49)
A)
25
2= 12.5
B)
-25; cannot be simplified
C)
–25 = –5
D)
1
25 =1
5
5
Divide and write in standard form.
50)
1+ 3i
5+ 6i
50)
A)
–23
11 + 9
11 i
B)
13
11 + 9
11 i
C)
– 13
61 – 21
61 i
D)
23
61 + 9
61 i
Find the quotient and write the answer in simplest form. Assume variables represent nonnegative values.
51)
8ab3
4a
51)
A)
b 2b
B)
b28b
C)
b22b
D)
b22ab
Find the perimeter.
52)
A triangle has sides measuring 480, 580, and 475 meters.
52)
A)
(36 5+ 20 3) meters
B)
(36 5+ 20) meters
C)
(56 5) meters
D)
(36 + 20 3) meters
Find the product and write the answer in simplest form. Assume variables represent nonnegative values.
53)
39xy ·34xy
53)
A)
336x2y2
B)
5xy
C)
6xy
D)
313x2y2
Use a calculator to approximate the root to the nearest thousandth.
54)
4101
54)
A)
3.192
B)
3.184
C)
3.170
D)
3.202
Divide and write in standard form.
55)
5– 3i
5+ 8i
55)
A)
– 49
39 – 55
39 i
B)
– 1
39 – 55
39 i
C)
1
89 – 55
89 i
D)
49
89 – 25
89 i
Use the rules of exponents to simplify. Write the answer with positive exponents. Assume that all variables represent
positive values.
56)
(x2/3)2/7
56)
A)
x4/21
B)
x4/7
C)
x2/3 ·x2/7
D)
x20/21
Solve.
57)
33x – 1=34x + 5
57)
A)
4
B)
– 2
C)
-6
D)
6
Find the domain.
58)
f(x) =3x – 17
58)
A)
{x|x 17} or (–
, 17]
B)
{x|x 17} or [17,
)
C)
{x|x -17} or (–
, -17]
D)
All real numbers or (–
,
)
6
Find the product and write the answer in simplest form. Assume variables represent nonnegative values.
59)
2y7
11 ·14y7
1331
59)
A)
2y77
121
B)
7y72
121
C)
y77
121
D)
14y7
121
Multiply.
60)
(8 – 6i)(9– 3i)
60)
A)
90 – 30i
B)
18i2– 78i + 72
C)
54 + 78i
D)
54 – 78i
Simplify. Assume variables represent nonnegative values.
61)
75
61)
A)
25 3
B)
8
C)
5
D)
5 3
Rewrite the following using radicals; then simplify if possible.
62)
165/4
62)
A)
5164=128
B)
4165=128
C)
5164=32
D)
4165=32
Find the root. Assume that variables represent nonnegative values.
63)
327k9
63)
A)
–3k3
B)
27k3
C)
3k12
D)
3k3
Solve.
64)
2x + 5 –x – 2 = 3
64)
A)
2, 38
B)
–2
C)
2
D)
3, 8
Multiply using FOIL. Assume all variables have nonnegative values.
65)
(39+3169)(33–313)
65)
A)
10 –3117+3507
B)
-10 –3117–3507
C)
-10 +3117–3507
D)
-10 –3117+3507
Solve.
66)
4x–1+ 7 = 0
66)
A)
No solution
B)
2401
C)
7
D)
– 2401
Find the root. Assume that variables represent any real number.
67)
(z – 3)2
67)
A)
z – 3
B)
z–3
C)
(z – 3)2
D)
z–3
Find the power of i.
68)
i–18
68)
A)
1
B)
–i
C)
i
D)
–1
7
Find the perimeter.
69)
69)
A)
26 6
B)
13 6
C)
9 6
D)
22 6
Rationalize the numerator. Assume that variables represent positive values.
70)
10 – 7
4
70)
A)
39
40 + 4 7
B)
93
40 + 4 7
C)
39
40 + 10 7
D)
107
40 + 10 7
Add or subtract. Assume that variables represent nonnegative values.
71)
5327x+ 5 364x
71)
A)
5391x
B)
353x
C)
35x
D)
73x
Solve the problem.
72)
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 13 feet and the height from the ground to the front doors is 8 feet,
how long is the ramp?
72)
A)
11.3 ft
B)
15.3 ft
C)
4.6 ft
D)
10.2 ft
Perform the indicated operations. Write the result using a radical. Assume that all variables represent positive values.
73)
7u·u
73)
A)
9u2
B)
14 u9
C)
92u
D)
7u2
Find the product and write the answer in simplest form. Assume variables represent nonnegative values.
74)
6·5
74)
A)
411
B)
430
C)
11
D)
30
Multiply.
75)
(7i)(–6i)
75)
A)
–13
B)
42
C)
–42
D)
13
76)
2i(8– 4i)
76)
A)
16i – 8i2
B)
16i – 8
C)
16i + 8i2
D)
8+ 16i
Rewrite the following using radicals; then simplify if possible. Assume that all variables represent nonnegative values.
77)
m7/6
77)
A)
m6m
B)
7m6
C)
6m7
D)
m7m6
8
Add or subtract. Assume that variables represent nonnegative values.
78)
44s+275s
78)
A)
711s
B)
7s 11
C)
-3s11
D)
-3 11s
Rationalize the denominator and simplify. Assume that variables represent positive values.
79)
c
c + d
79)
A)
c + d
c – d
B)
c – cd
c – d
C)
c + cd
c + d
D)
c – d
c – d
Add or subtract.
80)
(8 + 6i) – (-9 + i)
80)
A)
17 + 5i
B)
-1 + 7i
C)
17 – 5i
D)
–17 – 5i
Simplify. Assume that variables represent positive values.
81)
2025
81
81)
A)
5
B)
45
C)
25
D)
9
Write an expression in simplest form for the area of the figure.
82)
82)
A)
30 2
B)
180
C)
15 2
D)
10 3
Write the following in exponential form. Assume that all variables represent positive values.
83)
4c9
83)
A)
c9/4
B)
c4/9
C)
c-4/9
D)
c-9/4
Provide an appropriate response.
84)
True or false? The negative sixth root of 729 is –3.
84)
A)
True
B)
False
Multiply.
85)
(8 – 7i)2
85)
A)
64 – 161i
B)
64 – 63i
C)
15 – 112i
D)
113– 112i
Evaluate the root, if possible.
86)
–3216
86)
A)
6
B)
–6
C)
36
D)
–216
9
Rewrite the following using radicals; then simplify if possible. Assume that all variables represent nonnegative values.
87)
(64t12)1/2
87)
A)
8t12
B)
8t6
C)
64t12
D)
8 t12
Multiply the conjugates. Assume all variables have nonnegative values.
88)
(5 x +y)(5 x –y)
88)
A)
25x – 2 xy – y
B)
25x – y
C)
25x2–y2
D)
25x + y
Simplify. Assume variables represent nonnegative values.
89)
6x6y10z3
89)
A)
x6y4z3
B)
xyz6y4z3
C)
xy y4z3
D)
xy6y4z3
Rationalize the denominator. Assume variables represent non–negative values.
90)
4
3
90)
A)
4 3
3
B)
13
C)
16 3
3
D)
4 3
Solve. First isolate the radical term.
91)
42x – 12 +9=17
91)
A)
-3274
B)
2054
C)
22
D)
4108
Find the power of i.
92)
i12
92)
A)
i
B)
–i
C)
–1
D)
1
Simplify. Assume variables represent nonnegative values.
93)
348
93)
A)
632
B)
236
C)
6
D)
3
Add or subtract. Assume that variables represent nonnegative values.
94)
-12 10 – 15 10
94)
A)
–27 10
B)
310
C)
–210
D)
26 10
Rationalize the denominator. Assume variables represent non–negative values.
95)
6
3y
95)
A)
63y2
y
B)
63y2
C)
6y
D)
63y
y
10
Solve. First isolate the radical term.
96)
4k– 5 + 3 = 0
96)
A)
– 3
5
B)
– 81
5
C)
No solution
D)
81
5
Perform the indicated operations. Write the result using a radical. Assume that all variables represent positive values.
97)
5y8
7y8
97)
A)
2y8
B)
5y8
7y8
C)
35 y16
D)
12 y8
Simplify. Assume variables represent nonnegative values.
98)
4324
98)
A)
443
B)
344
C)
18
D)
4
Solve.
99)
10 + x +11 – 5x = –1
99)
A)
0
B)
1
C)
11
2
D)
No solution
Rationalize the denominator and simplify. Assume that variables represent positive values.
100)
3 x
x+ 2 y
100)
A)
3x + 6 xy
x + 4y
B)
3x + 6 xy
x + 2y
C)
3x – 6 xy
x – 2y
D)
3x – 6 xy
x – 4y
Add or subtract. Assume that variables represent nonnegative values.
101)
147+ 5 108
101)
A)
12 3
B)
–3
C)
13 3
D)
37 3
Rationalize the denominator. Assume variables represent non–negative values.
102)
14
14
102)
A)
14
B)
1
C)
14 14
D)
14
Find the domain.
103)
f(x) =x + 2
103)
A)
{x|x -2} or [-2,
)
B)
{x|x 2} or (–
, 2]
C)
{x|x 2} or [2,
)
D)
{x|x -2} or (–
, -2]
11
Multiply using FOIL. Assume all variables have nonnegative values.
104)
(3100+ 7)(3100 – 1)
104)
A)
10310 + 63100– 7
B)
10310 + 63100+ 7
C)
10310 + 83100– 7
D)
310,000 + 63100 – 7
Rationalize the denominator. Assume variables represent non–negative values.
105)
98
x
105)
A)
7x
x
B)
72
x
C)
72x
D)
72x
x
Simplify. Assume that variables represent positive values.
106)
5
36
106)
A)
6 5
B)
36 5
C)
5
36
D)
5
6
Use the distributive property. Assume that variables represent nonnegative values.
107)
7( 2 – 3 21)
107)
A)
14 – 21 3
B)
14 – 3 147
C)
14 + 21 3
D)
14 + 3 147
Simplify.
108)
3·21 +8·14
108)
A)
9 7
B)
7 7
C)
5 7
D)
3 7 +228
Provide an appropriate response.
109)
True or false? The negative square root of 16 is 4.
109)
A)
True
B)
False
Simplify. Assume variables represent nonnegative values.
110)
38a8b5
110)
A)
2ab3a2b2
B)
23a2b2
C)
2a2b3a2b2
D)
2ab3a3b3
Add or subtract.
111)
(9 – 9i) + (5+ 4i)
111)
A)
14 + 5i
B)
4+ 13i
C)
–14 + 5i
D)
14 – 5i
Provide an appropriate response.
112)
True or false? 11 is simplified.
112)
A)
True
B)
False
12
Solve the problem.
113)
A diagonal crosswalk at an intersection of First Street and Grand Avenue is the hypotenuse of a
triangle in which crosswalks across each street are the legs. First Street is 27 feet wide and Grand
Avenue is 46 feet wide. How much shorter is the distance traveled by pedestrians using the
diagonal crosswalk rather than using both crosswalks that form the legs of the triangle.
113)
A)
7.3 feet
B)
19 feet
C)
53.3 feet
D)
19.7 feet
Use the rules of exponents to simplify. Write the answer with positive exponents. Assume that all variables represent
positive values.
114)
(b7/4)4
114)
A)
b1/4
B)
b11/4
C)
b7/16
D)
b7
Simplify. Assume that variables represent positive values.
115)
119
7
115)
A)
7
B)
17
C)
17
D)
7
Find all square roots of the number.
116)
100
116)
A)
±9
B)
±11
C)
±1
D)
±10
Provide an appropriate response.
117)
True or false? The principal fifth root of –243 is 3.
117)
A)
True
B)
False
Solve.
118)
6q – 5=5
118)
A)
No solution
B)
10
3
C)
5
D)
25
Evaluate the root, if possible.
119)
–1.21
119)
A)
Not real
B)
–0.11
C)
–1.1
D)
1.1
Provide an appropriate response.
120)
True or false? The principal square root of 49 is 7.
120)
A)
True
B)
False
Multiply using FOIL. Assume all variables have nonnegative values.
121)
(3 +d)(6 –d)
121)
A)
18 + 3 d–d
B)
18 – 3 d+d
C)
18 + 3 d+d
D)
18 – 3 d–d
Evaluate the root, if possible.
122)
5– 1024
122)
A)
–2
B)
–4
C)
Not real
D)
4
13
Rationalize the denominator. Assume variables represent non–negative values.
123)
121
3
123)
A)
11 3
3
B)
121 3
3
C)
20
D)
11 3
Find the product.
124)
(2 – 5 5)2
124)
A)
129–20 5
B)
4+25 5
C)
4–25 5
D)
129+20 5
Use the rules of exponents to simplify. Write the answer with positive exponents. Assume that all variables represent
positive values.
125)
x1/3·x2/3
125)
A)
x
B)
x2/9
C)
x2/3
D)
x-1
Use a calculator to approximate the root to the nearest thousandth.
126)
–468
126)
A)
-2.858
B)
-2.872
C)
-2.850
D)
-2.840
Solve.
127)
x + 6 +2 – x = 4
127)
A)
–2
B)
31, –2
C)
0
D)
2, –2
128)
3t=-2
128)
A)
-6
B)
3-2
C)
-8
D)
no real–number solution
Write the following in exponential form. Assume that all variables represent positive values.
129)
72t – 8)8
129)
A)
(2t – 8)-7/8
B)
1
(2t – 8)8/7
C)
(2t – 8)8/7
D)
(2t – 8)7/8
Evaluate the root, if possible.
130)
–625
130)
A)
–25
B)
25
C)
Not real
D)
312
Add or subtract. Assume that variables represent nonnegative values.
131)
611 +311
131)
A)
99
B)
18 11
C)
911
D)
922
14
Find the quotient and write the answer in simplest form. Assume variables represent nonnegative values.
132)
15 18z11
5 2z5
132)
A)
3z3
B)
9z3z
C)
9z3
D)
9z6
Find the domain.
133)
f(x) =x – 5
133)
A)
{x|x -5} or [-5,
)
B)
All real numbers or (–
,
)
C)
{x|x
0} or [0,
)
D)
{x|x 5} or [5,
)
Solve.
134)
2k + 1 = –15
134)
A)
–112
B)
224
C)
112
D)
no real–number solution
Find the root. Assume that variables represent any real number.
135)
3–343x3
135)
A)
–7x3
B)
–7x
C)
–7 x
D)
–49x
Perform the indicated operations. Write the result using a radical. Assume that all variables represent positive values.
136)
6u5
8u3
136)
A)
6u5
8u3
B)
u
C)
48 u22
D)
24 u11
Use the rules of exponents to simplify. Write the answer with positive exponents. Assume that all variables represent
positive values.
137)
(32k5m–10)1/5
137)
A)
2km2
B)
2km-2
C)
5km2
D)
5km-2
Rewrite the following using radicals; then simplify if possible. Assume that all variables represent nonnegative values.
138)
23s1/2
138)
A)
s23
B)
23s
C)
23 s
D)
23s
Rationalize the denominator and simplify. Assume that variables represent positive values.
139)
7n
m – 21n
139)
A)
7mn + 7n 3
m – 21n
B)
7mn – 7n 3
m + 21n
C)
7mn + 21
m + 21n
D)
7mn – 7n 3
m – 7n
15
Rationalize the numerator. Assume that variables represent positive values.
140)
8x
7
140)
A)
7x
8x
B)
1
7 8x
C)
7x
8 7x
D)
8x
7 8x
141)
6
5
141)
A)
6
5 6
B)
5
6 b
C)
1
5
D)
1
5 6
Represent the radical as a radical with a smaller root index. Assume any variables represent nonnegative values.
142)
636
142)
A)
336
B)
6
C)
36
D)
46
Find the product and write the answer in simplest form. Assume variables represent nonnegative values.
143)
x6
13 ·x9
13
143)
A)
x7x
13
B)
x8x
13
C)
x7
13
D)
x7x
169
Multiply the conjugates. Assume all variables have nonnegative values.
144)
( 5x + y)( 5x – y)
144)
A)
x + 2y 5
B)
6x
C)
5x –y2
D)
x – 2y 5
145)
(4 +7)(4 –7)
145)
A)
23 +8 7
B)
23 –8 7
C)
9
D)
23
Evaluate the root, if possible.
146)
0.25
146)
A)
0.05
B)
0.5
C)
0.6
D)
5
Multiply.
147)
(4 – 7i)(7+ 6i)
147)
A)
-42i2– 25i + 28
B)
-14 – 73i
C)
70 + 25i
D)
70 – 25i
Rewrite the following using radicals; then simplify if possible. Assume that all variables represent nonnegative values.
148)
2w2/7
148)
A)
27w2
B)
22w7
C)
22w7
D)
72w2
Evaluate the root, if possible.
149)
25
149)
A)
Not real
B)
6
C)
5
D)
12
16
Provide an appropriate response.
150)
Can the following be simplified without first simplifying the individual radical expressions?
712 2+512 2
150)
A)
No
B)
Yes
Use a graphing calculator to graph the function.
151)
f(x) =x + 5
151)
A)
B)
C)
D)
Solve.
152)
9h – 3 =5h + 6
152)
A)
9
14
B)
4
9
C)
3
4
D)
9
4
17
Add or subtract. Assume that variables represent nonnegative values.
153)
73m7p5– 5m2p3mp2
153)
A)
12m2p3mp2
B)
2m2p3mp2
C)
2
D)
cannot combine because the radicals are not like
Evaluate the root, if possible.
154)
–0.0025
154)
A)
Not real
B)
–0.005
C)
0.05
D)
–0.05
Rewrite the following using radicals; then simplify if possible.
155)
6251/2
155)
A)
625=12.5
B)
625=625
C)
625=25
D)
625=50
Find the product.
156)
(7 + 3)2
156)
A)
52 +14 3
B)
49 +14 3
C)
52 +7 3
D)
10 +14 3
Find the power of i.
157)
i21
157)
A)
–i
B)
1
C)
i
D)
–1
Rationalize the denominator. Assume variables represent non–negative values.
158)
4
21
158)
A)
421
21
B)
16 21
21
C)
421
D)
445
Find the root. Assume that variables represent nonnegative values.
159)
0.49r16s8
159)
A)
7r16s8
B)
7r8s4
C)
0.7r16s8
D)
0.7r8s4
Divide and write in standard form.
160)
29 + 11i
6 + i
160)
A)
6
35 +i
35
B)
5
37 +11i
37
C)
6– 1
D)
5+ i
18
Evaluate the root, if possible.
161)
4256
625
161)
A)
64
125
B)
16
25
C)
256
625
D)
4
5
Multiply using FOIL. Assume all variables have nonnegative values.
162)
(4 r –s)(5 r – 5 s)
162)
A)
20r– 25 rs– 5s
B)
20r+ 25 rs+ 5s
C)
20r– 25 rs+ 5s
D)
20r+ 25 rs– 5s
163)
(3 17 + –513)(2 2 +-2 7)
163)
A)
634 – 6 119– 10 26 + 10 91
B)
634 – 6 119– 5 26 + 10 91
C)
634 – 6 119– 10 26 – 2 91
D)
634 – 2 119– 10 26 + 10 91
Write the following in exponential form. Assume that all variables represent positive values.
164)
2m5
164)
A)
m2/5
B)
m5/2
C)
–m5/2
D)
m-5/2
Add or subtract.
165)
(3 + 6i) – (4+ 6i) + (9+ 2i)
165)
A)
8+ 14i
B)
-10 + 2i
C)
-10 – 2i
D)
8+ 2i
Find the indicated value of the function.
166)
f(x) =4x – 14, find f(12).
166)
A)
34
B)
33
C)
233
D)
35
Rationalize the denominator. Assume variables represent non–negative values.
167)
64
5
167)
A)
8 5
B)
8 5
5
C)
64 5
5
D)
33
Solve.
168)
x= –9
168)
A)
–81
B)
81
C)
9
D)
no real–number solution
Divide and write in standard form.
169)
8+ 2i
6– 8i
169)
A)
64
25 + 52
25 i
B)
8
25 + 19
25 i
C)
– 2
7+ 19
28 i
D)
– 16
7+ 19
28 i
19
Evaluate the root, if possible.
170)
49
100
170)
A)
7
11
B)
12
25
C)
4
5
D)
7
10
Rewrite the following using radicals; then simplify if possible. Assume that all variables represent nonnegative values.
171)
x1/7
171)
A)
x
B)
x7
C)
1
7x
D)
7x
Multiply using FOIL. Assume all variables have nonnegative values.
172)
( 5 + 2)( 6– 5)
172)
A)
30 – 10
B)
30 – 3 6– 10
C)
30 – 5 5+ 2 6– 10
D)
-2 30 – 10
Rationalize the denominator. Assume variables represent non–negative values.
173)
4 2y7
32y3
173)
A)
2y
B)
y2
4
C)
y
48
D)
y
2
Solve the problem.
174)
The distance d in miles that can be seen on the surface of the ocean is given by d = 1.3 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 14.5 miles?
174)
A)
210 ft
B)
273 ft
C)
124 ft
D)
112 ft
Rationalize the numerator. Assume that variables represent positive values.
175)
2x + 5
9
175)
A)
2x – 5
9( 2x – 5)
B)
2x – 5
9( 2x + 5)
C)
2x – 25
9( 2x + 5)
D)
2x – 25
9( 2x – 5)
Rationalize the denominator and simplify. Assume that variables represent positive values.
176)
3
5 – 2
176)
A)
15 + 3 2
23
B)
15 – 3 2
23
C)
3
5–32
D)
15 + 3 2
-3
Add or subtract.
177)
[(1+ 8i) – (8+ 9i)] – (1– 6i)
177)
A)
-8 + 5i
B)
-8 + 11i
C)
10 + 11i
D)
10 + 5i
20
Find the indicated value of the function.
178)
f(x) =–3x + 7, find f(0)
178)
A)
Not real
B)
7
C)
7
D)
11
Find the power of i.
179)
i–12
179)
A)
i
B)
–1
C)
1
D)
–i
Evaluate the root, if possible.
180)
–81
180)
A)
Not real
B)
–40
C)
–9
D)
9
Solve.
181)
41 – 2x + 3 =9 – 2x + 7
181)
A)
7
2
B)
no solution
C)
5
2
D)
55
2
Evaluate the root, if possible.
182)
–3-125
182)
A)
11
B)
–5
C)
–25
D)
5
183)
38
183)
A)
4
B)
3
C)
2
D)
-2
Multiply the conjugates. Assume all variables have nonnegative values.
184)
(2 7 –813)(2 7 +813)
184)
A)
-804
B)
860+ 32 91
C)
-90
D)
860
Find the perimeter.
185)
A lot has sides measuring 550, 518, 332, and 475 yards.
185)
A)
(52 + 20 3) yards
B)
(72 2) yards
C)
(52 2+ 20 3) yards
D)
(104+ 20 3) yards
Use the rules of exponents to simplify. Write the answer with positive exponents. Assume that all variables represent
positive values.
186)
(5v5/2)2
v3
186)
A)
25
v2
B)
25v2
C)
5v2
D)
25v5
Solve.
187)
2x + 3 –x + 1 = 1
187)
A)
–3, –1
B)
No solution
C)
3, –1
D)
3
21
Find the root. Assume that variables represent any real number.
188)
–x16
188)
A)
– x8
B)
x8
C)
– x8
D)
–x8
Solve.
189)
2k + 1 =13
189)
A)
84
B)
–84
C)
42
D)
168
Simplify. Assume that variables represent positive values.
190)
3686
32
190)
A)
9
B)
6
C)
8
D)
7
Use the distributive property. Assume that variables represent nonnegative values.
191)
211(411 + 3 33)
191)
A)
-88 + 66 3
B)
88 – 66 3
C)
88 + 6 363
D)
88 + 66 3
Represent the radical as a radical with a smaller root index. Assume any variables represent nonnegative values.
192)
449a2r18
192)
A)
7ar9
B)
49a2r9
C)
49a2r18
D)
7ar18
Divide and write in standard form.
193)
13
3 + 2i
193)
A)
1
2+i
2
B)
3+2i
C)
3–2i
D)
–1
2+13
2
Represent the radical as a radical with a smaller root index. Assume any variables represent nonnegative values.
194)
6a2
194)
A)
3a
B)
4a
C)
a2
D)
a
195)
44w14
195)
A)
4w14
B)
4w7
C)
2w14
D)
2w7
Find the root. Assume that variables represent any real number.
196)
144y6
196)
A)
12y3
B)
12y2
C)
12 y3
D)
12 y
Add or subtract. Assume that variables represent nonnegative values.
197)
-5 45 + 4 847 –20 + 3 175
197)
A)
17 5+ 59 7
B)
-17 5+ 59 7
C)
17 5– 59 7
D)
-17 5– 59 7
22
Find the power of i.
198)
i–3
198)
A)
–i
B)
i
C)
1
D)
–1
Multiply.
199)
(6 + 6i)(2+ 4i)
199)
A)
–12 + 36i
B)
24i2+ 36i + 12
C)
36 – 12i
D)
–12 – 36i
Write the imaginary number using i.
200)
–276
200)
A)
2i 69
B)
269
C)
–2i 69
D)
–269
Multiply.
201)
(8i)(9i)
201)
A)
–72
B)
–17
C)
17
D)
72
Find the root. Assume that variables represent any real number.
202)
–4x4
202)
A)
-|x|
B)
-x
C)
x
D)
-x
Solve the problem.
203)
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 25 m high and the driveway is 49 m from the building,
how long is the string of banners?
203)
A)
35.4 m
B)
55.0 m
C)
8.6 m
D)
42.1 m
Solve.
204)
q + 1=6
204)
A)
36
B)
35
C)
37
D)
49
Find the root. Assume that variables represent nonnegative values.
205)
3x15
205)
A)
x45
B)
3z
C)
z
3
D)
x5
Solve. First isolate the radical term.
206)
9x – 3 – 3 = 0
206)
A)
2
3
B)
9
C)
No solution
D)
4
3
Rationalize the denominator. Assume variables represent non–negative values.
207)
710x
x3
207)
A)
7x 10
B)
710x
x
C)
710
x
D)
70
x
23
Use a calculator to approximate the root to the nearest thousandth.
208)
3
208)
A)
1.732
B)
1.729
C)
1.737
D)
3.000
Find the root. Assume that variables represent nonnegative values.
209)
z6
209)
A)
2z
B)
z
2
C)
z3
D)
z12
Rewrite the following using radicals; then simplify if possible.
210)
274/3
210)
A)
3274=81
B)
4273=81
C)
4273=243
D)
3274=243
Write the imaginary number using i.
211)
––240
211)
A)
–415
B)
4i 15
C)
415
D)
–4i 15
Find the quotient and write the answer in simplest form. Assume variables represent nonnegative values.
212)
32
2
212)
A)
42
B)
4
C)
4 2
D)
2
Simplify.
213)
9 5 ·55 +255 ·45
213)
A)
45 11 +10 99
B)
77 11
C)
75 11
D)
73 11
Simplify. Assume that variables represent positive values.
214)
25
64
214)
A)
40
B)
5
8
C)
8
5
D)
25
8
Add or subtract.
215)
(6 – 3i) + (3+ 9i)
215)
A)
–9– 6i
B)
9+ 6i
C)
3+ 12i
D)
9– 6i
Evaluate the root, if possible.
216)
3– 8
125
216)
A)
–8
125
B)
4
25
C)
2
5
D)
–2
5
24
217)
– 625
36
217)
A)
–25
6
B)
Not real
C)
25
6
D)
–52
3
Rewrite the following using radicals; then simplify if possible.
218)
12961/4
218)
A)
41296 =6
B)
41296 =7776
C)
41296 =144
D)
41296 =24
Find the product and write the answer in simplest form. Assume variables represent nonnegative values.
219)
3
17 ·11
13
219)
A)
33
7293
B)
33
221
C)
7293
221
D)
33
221
Simplify. Assume variables represent nonnegative values.
220)
3512x4y5
220)
A)
xy3xy2
B)
8xy3x2y
C)
8xy3xy
D)
8xy3xy2
Solve the problem.
221)
The manufacturer’s cost, C, in dollars, can be found using the formula C = 5003n+ 1700, where n is
he number of parts produced. Find the cost when 729 parts are produced.
221)
A)
$15,200
B)
$6200
C)
$3950
D)
$56
Find the root. Assume that variables represent any real number.
222)
–4x36
222)
A)
–x9
B)
x9
C)
– x9
D)
–x9
Rationalize the denominator and simplify. Assume that variables represent positive values.
223)
5+ 6
7– 9
223)
A)
35 – 54 + 6 7– 9 5
-74
B)
35 + 54 + 6 7+ 9 5
88
C)
35 – 54 + 6 7– 9 5
88
D)
35 + 54 + 6 7+ 9 5
-74
Find all square roots of the number.
224)
81
224)
A)
±18
B)
±9
C)
±10
D)
±11
25
Find the domain.
225)
f(x) =8x + 9
225)
A)
x|x – 9
8 or – 9
8,
B)
x|x – 9
8 or –, – 9
8
C)
x|x 9
8 or 9
8,
D)
x|x 9
8 or –, 9
8
Perform the indicated operations. Write the result using a radical. Assume that all variables represent positive values.
226)
4t·3t2
226)
A)
12 t3
B)
7t3
C)
7t2
D)
12 t11
Use the distributive property. Assume that variables represent nonnegative values.
227)
2( 2 –22)
227)
A)
2+211
B)
2–44
C)
2–11 2
D)
2–211
Use a calculator to approximate the root to the nearest thousandth.
228)
–31
228)
A)
–31.000
B)
–5.568
C)
–5.573
D)
–5.565
Find the quotient and write the answer in simplest form. Assume variables represent nonnegative values.
229)
x5y7
x3y2
229)
A)
xy2x
B)
xy2y
C)
x2y y
D)
xy y
Rationalize the denominator. Assume variables represent non–negative values.
230)
8
23
230)
A)
64 23
23
B)
823
C)
537
D)
823
23
Multiply the conjugates. Assume all variables have nonnegative values.
231)
(13 –3)( 13 +3)
231)
A)
10
B)
16 – 2 39
C)
16 + 2 39
D)
16
Provide an appropriate response.
232)
Can the following be simplified to an expression involving a single radical?
x3135+32560x3
232)
A)
Yes
B)
No
Perform the indicated operations. Write the result using a radical. Assume that all variables represent positive values.
233)
512 ·2
233)
A)
79
B)
10 24
C)
10 4608
D)
724
26
Add or subtract. Assume that variables represent nonnegative values.
234)
1233+ 1533
234)
A)
2736
B)
2739
C)
2733
D)
33
Provide an appropriate response.
235)
True or false? (-2)(-8) = 4
235)
A)
True
B)
False
Add or subtract. Assume that variables represent nonnegative values.
236)
-4w247w3– 6w247w3
236)
A)
-10w247w3
B)
10w247w3
C)
cannot combine because the radicals are not like
D)
-10w347w
Add or subtract.
237)
3i + (-7 – i)
237)
A)
7– 4i
B)
–7+ 2i
C)
7– 2i
D)
–7+ 4i
Rewrite the following using radicals; then simplify if possible.
238)
–2891/2
238)
A)
–289= –34
B)
–289= –17
C)
–289; cannot be simplified
D)
–289 = –8.5
Write an expression in simplest form for the area of the figure.
239)
239)
A)
15 12
B)
8 6
C)
15 3
D)
30 3
Find the perimeter.
240)
240)
A)
13 2+ 4 8
B)
21 2
C)
42
D)
932
Multiply using FOIL. Assume all variables have nonnegative values.
241)
( 2 +5)( 5 +3)
241)
A)
10 +6+6+15
B)
10 +6+5+15
C)
10 +6+25 +15
D)
10 +6+5+15
27
Solve.
242)
3x + 1 = 3 +x – 4
242)
A)
–1
B)
–5, –8
C)
No solution
D)
5, 8
Find the power of i.
243)
i19
243)
A)
1
B)
–i
C)
–1
D)
i
Find the product and write the answer in simplest form. Assume variables represent nonnegative values.
244)
13
23 ·8
23
244)
A)
104
23
B)
104
23
C)
2598
23
D)
226
23
Use a calculator to approximate the root to the nearest thousandth.
245)
3–96
245)
A)
-4.575
B)
-4.579
C)
-4.588
D)
-4.583
Evaluate the root, if possible.
246)
3-125
246)
A)
25
B)
11
C)
–5
D)
5
Write the following as a single radical. Assume that all variables represent nonnegative values.
247)
83z
247)
A)
(8z)3
B)
3z
C)
24 z
D)
(3z)8
Divide and write in standard form.
248)
8+ 2i
4+ 7i
248)
A)
18
65 – 64
65 i
B)
46
65 – 48
65 i
C)
– 46
33 – 16
11 i
D)
– 6
11 – 16
11 i
Find the quotient and write the answer in simplest form. Assume variables represent nonnegative values.
249)
18b
3b
249)
A)
6 b
B)
6b
C)
6
D)
6
Rationalize the denominator and simplify. Assume that variables represent positive values.
250)
5
7 + 6
250)
A)
35 – 6 5
13
B)
35 + 6 5
-29
C)
35 – 6 5
-29
D)
335 + 7 5
42
28
Solve.
251)
13 – 3x =x – 2
251)
A)
15
B)
No solution
C)
15
4
D)
5
Multiply the conjugates. Assume all variables have nonnegative values.
252)
( 5 + 1)( 5– 1)
252)
A)
6
B)
4+ 2 5
C)
4– 2 5
D)
4
Add or subtract.
253)
(9 + 5i) – (-8 + i)
253)
A)
1+ 6i
B)
17 – 4i
C)
–17 – 4i
D)
17 + 4i
Solve.
254)
x=5
254)
A)
5
B)
25
C)
10
D)
–25
Find the product and write the answer in simplest form. Assume variables represent nonnegative values.
255)
14m5·7m15
255)
A)
14m77
B)
7m92
C)
7m11
D)
7m10 2
Rewrite the following using radicals; then simplify if possible.
256)
(-32)1/5
256)
A)
–532 = –16
B)
5-32 =-2
C)
–532 =-8
D)
5-32 =-8
Represent the radical as a radical with a smaller root index. Assume any variables represent nonnegative values.
257)
12 x8
257)
A)
3x2
B)
x2
C)
4x2
D)
4x
Simplify. Assume that variables represent positive values.
258)
4 7r2
625s8
258)
A)
47s2
5r2
B)
47r2
5s4
C)
47r2
5s2
D)
47r2
25s2
Write the imaginary number using i.
259)
–81
259)
A)
–9i
B)
±9
C)
i 9
D)
9i
29
Rewrite the following using radicals; then simplify if possible.
260)
31254/5
260)
A)
531254=625
B)
431255=78,125
C)
431255=625
D)
531254=78,125
Find the product and write the answer in simplest form. Assume variables represent nonnegative values.
261)
34x ·39x
261)
A)
6x
B)
5x
C)
336x2
D)
313x2
Write the imaginary number using i.
262)
–2500
262)
A)
–50i
B)
i50
C)
±50
D)
50i
Find the product and write the answer in simplest form. Assume variables represent nonnegative values.
263)
5x2z3·5x28z29
263)
A)
x7z75z2
B)
x7z65z
C)
x6z65z
D)
x6z65z2
Solve the problem.
264)
Find the distance an object has fallen after 6 seconds. Use the formula t =h
16, where t is the time
in seconds that it takes an object to fall a distance of h feet.
264)
A)
144 ft
B)
9.8 ft
C)
576 ft
D)
0.61 ft
Rewrite the following using radicals; then simplify if possible. Assume that all variables represent nonnegative values.
265)
z6
144
1/2
265)
A)
z3
144
B)
z6
12
C)
z6
144
D)
z3
12
Provide an appropriate response.
266)
True or false? 25 ·4=25 · 4
266)
A)
True
B)
False
Find the root. Assume that variables represent any real number.
267)
(2y – 7)2
267)
A)
2y – 7
B)
4y2– 28y + 49
C)
4y2– 28y + 49
D)
2y – 7
Rationalize the denominator. Assume variables represent non–negative values.
268)
31296x4
6x
268)
A)
6x3x
B)
6x36
C)
x3216
D)
6x
30
Evaluate the root, if possible.
269)
4256
269)
A)
4
B)
16
C)
5
D)
3
Solve. First isolate the radical term.
270)
4k– 1 + 4 = 0
270)
A)
No solution
B)
256
C)
– 256
D)
– 4
Write the following in exponential form. Assume that all variables represent positive values.
271)
x7
271)
A)
x-7/2
B)
-x2/7
C)
x-2/7
D)
x7/2
Solve.
272)
3x + 10 = 5 – 2x
272)
A)
5
4, 9
B)
3
4
C)
5
D)
3
4, 5
Rationalize the denominator. Assume variables represent non–negative values.
273)
3 3
5
273)
A)
375
5
B)
3375
5
C)
75
5
D)
315
5
Use a calculator to approximate the root to the nearest thousandth.
274)
713
274)
A)
713.000
B)
26.707
C)
26.699
D)
26.702
Write the imaginary number using i.
275)
–256
275)
A)
–16i
B)
–i16
C)
16i
D)
±16
Find the root. Assume that variables represent nonnegative values.
276)
481a4
276)
A)
3a2
B)
3 a
C)
81a
D)
3a
Find the domain.
277)
f(x) =4x – 3
277)
A)
All real numbers or (–
,
)
B)
{x|x
0} or [0,
)
C)
{x|x 3} or [3,
)
D)
{x|x -3} or [-3,
)
Find the quotient and write the answer in simplest form. Assume variables represent nonnegative values.
278)
10 15
2 5
278)
A)
5 3
B)
5 5
C)
15
D)
2 3
31
Add or subtract. Assume that variables represent nonnegative values.
279)
-7t247t3+ 4t237t3
279)
A)
-3t347t
B)
-3t247t3
C)
3t247t3
D)
cannot combine because the radicals are not like
Use the rules of exponents to simplify. Write the answer with positive exponents. Assume that all variables represent
positive values.
280)
y5/3
y1/3
280)
A)
y-1/2
B)
y1/2
C)
y5/3
D)
y
Use a graphing calculator to graph the function.
281)
f(x) =4x + 4
281)
A)
B)
C)
D)
32
Find the product and write the answer in simplest form. Assume variables represent nonnegative values.
282)
7
5·1
5
282)
A)
7
10
B)
7
25
C)
5
7
D)
7
5
Multiply.
283)
(6 + 3i)(6– 5i)
283)
A)
51 + 12i
B)
-15i2– 12i + 36
C)
21 + 48i
D)
51 – 12i
Add or subtract. Assume that variables represent nonnegative values.
284)
84x7– 3x4x3
284)
A)
84x7– 3x4x3
B)
114x3
C)
5x4x7
D)
5x4x3
Divide and write in standard form.
285)
9+ 5i
5– 7i
285)
A)
5
37 + 44
37 i
B)
– 10
3+ 11
6i
C)
80
37 + 38
37 i
D)
– 5
24 + 11
6i
Find the domain.
286)
f(x) =– 9x + 2
286)
A)
x|x – 2
9 or – 2
9,
B)
x|x 2
9 or 2
9,
C)
x|x 2
9 or –,2
9
D)
x|x < 2
9or –,2
9
Solve.
287)
x + 3 = x – 3
287)
A)
6
B)
1, 13
C)
1, 6
D)
6, 13
Add or subtract.
288)
(-3 + 4i) – 2
288)
A)
-5 + 4i
B)
-1 – 4i
C)
5– 4i
D)
-1 + 4i
Find the quotient and write the answer in simplest form. Assume variables represent nonnegative values.
289)
152 42
19 6
289)
A)
8 7
B)
8 6
C)
19 7
D)
56
Solve.
290)
3x + 7=5
290)
A)
125
B)
-2
C)
118
D)
18
33
Evaluate the root, if possible.
291)
–41296
291)
A)
–6
B)
Not real
C)
–36
D)
–5
Find the product and write the answer in simplest form. Assume variables represent nonnegative values.
292)
3175·325
292)
A)
10315
B)
10335
C)
5335
D)
5325
Find the quotient and write the answer in simplest form. Assume variables represent nonnegative values.
293)
20
5
293)
A)
5
B)
2
C)
2 5
D)
25
Represent the radical as a radical with a smaller root index. Assume any variables represent nonnegative values.
294)
4100
294)
A)
10
B)
310
C)
100
D)
410
Solve.
295)
2x + 3 +4 – x = 4
295)
A)
3, 11
9
B)
–3
C)
3
D)
No solution
Find the root. Assume that variables represent any real number.
296)
3x15
296)
A)
x5
B)
x5
C)
– x5
D)
–x5
Provide an appropriate response.
297)
True or false? 81 =9
297)
A)
True
B)
False
Solve.
298)
x + 7 + 5 = x
298)
A)
2
B)
9
C)
2, 9
D)
9, 18
Find the product.
299)
(57– 4 13)2
299)
A)
-17 – 40 91
B)
383– 40 91
C)
383– 20 91
D)
383
Rewrite the following using radicals; then simplify if possible.
300)
7291/3
300)
A)
3729=9
B)
3729=6561
C)
3729=19,683
D)
3729=27
34
Rationalize the denominator. Assume variables represent non–negative values.
301)
45x3
y5
301)
A)
x45xy
y3
B)
3x 5xy
y3
C)
3x35
y5
D)
3x
y25x
y
Solve the problem.
302)
The cost, C, of producing n clocks can be found using the formula C = 16 n + 64. What is the cost
when no clocks are produced?
302)
A)
16
B)
32
C)
128
D)
1024
Find the power of i.
303)
i–13
303)
A)
i
B)
–i
C)
1
D)
–1
Simplify. Assume variables represent nonnegative values.
304)
125k7q8
304)
A)
5k3q45
B)
5k3q45k
C)
5k2q45k
D)
5k7q85k
Perform the indicated operations. Write the result using a radical. Assume that all variables represent positive values.
305)
32·412
305)
A)
12 24
B)
724
C)
12 27,648
D)
727,648
Solve.
306)
7a – 3 =2a + 5
306)
A)
2
5
B)
8
9
C)
5
8
D)
8
5
Find the indicated value of the function.
307)
f(x) =-5x + 9, find f(0)
307)
A)
4
B)
3
C)
2
D)
9
Rationalize the denominator. Assume variables represent non–negative values.
308)
34
9x2
308)
A)
3324x
81
B)
312x
3x
C)
3324x2
9x
D)
336x
9x
Add or subtract. Assume that variables represent nonnegative values.
309)
63 –175
309)
A)
-16 7
B)
-14
C)
8 7
D)
-2 7
35
Write the following as a single radical. Assume that all variables represent nonnegative values.
310)
47n
310)
A)
14 n
B)
11 n
C)
28 n
D)
n28
Find the product and write the answer in simplest form. Assume variables represent nonnegative values.
311)
2·3 x3
311)
A)
3 2x3
B)
18x3
C)
x18x
D)
3x 2x
Simplify.
312)
1225
7–363
312)
A)
14 7
B)
27
C)
8 7
D)
-4 7
Use a graphing calculator to graph the function.
313)
f(x) =3x + 3
313)
A)
B)
C)
D)
36
Write the imaginary number using i.
314)
–160
314)
A)
4i 10
B)
–410
C)
410
D)
–4i 10
Solve the problem.
315)
Find the skid distance after braking hard at a speed of 75 miles per hour. Use the formula
S = 7
22D, where D represents the skid distance in feet on asphalt and S represents the speed of the
car in miles per hour.
315)
A)
459.18 ft
B)
229.59 ft
C)
42.87 ft
D)
918.37 ft
Add or subtract. Assume that variables represent nonnegative values.
316)
5 t +4 t
316)
A)
9 t
B)
10 t
C)
t
D)
8 t
Find the root. Assume that variables represent nonnegative values.
317)
–3–125x3
317)
A)
–5x
B)
5x3
C)
5x
D)
–125x
Find the product and write the answer in simplest form. Assume variables represent nonnegative values.
318)
42·44
318)
A)
86
B)
46
C)
2
D)
48
Find the perimeter.
319)
A rectangular coal bin has a length of 50 feet and a width of 32 feet.
319)
A)
9 2 feet
B)
9 4 feet
C)
18 2 feet
D)
18 4 feet
Divide and write in standard form.
320)
3
i
320)
A)
3i
B)
3– i
C)
–3i
D)
i –3
Add or subtract. Assume that variables represent nonnegative values.
321)
-8 48 – 5 243+ 4 108
321)
A)
281 3
B)
-8 3
C)
-281 3
D)
-53 3
Represent the radical as a radical with a smaller root index. Assume any variables represent nonnegative values.
322)
664
322)
A)
4
B)
44
C)
64
D)
34
Simplify. Assume variables represent nonnegative values.
323)
192x2
323)
A)
192x
B)
8x 3
C)
8 3x
D)
8x
37
Find the power of i.
324)
i22
324)
A)
i
B)
1
C)
–1
D)
–i
Use the rules of exponents to simplify. Write the answer with positive exponents. Assume that all variables represent
positive values.
325)
1210/13
12–4/13
325)
A)
12–40/169
B)
1210/13 –124/13
C)
126/13
D)
1214/13
Solve the problem.
326)
The time T in seconds for a pendulum of length L feet to make one swing is given by
T = 2L
41.How long is a pendulum (to nearest hundredth) if it makes one swing in 1.2 seconds?
Use 3.14 for .
326)
A)
1.5 ft
B)
9.4 ft
C)
59.04 ft
D)
14.76 ft
Add or subtract. Assume that variables represent nonnegative values.
327)
-5 19 + 3 17 – 2 19 – 7 17
327)
A)
-7 19 + 4 17
B)
719 – 4 17
C)
-7 19 – 4 17
D)
719 + 4 17
Rationalize the denominator and simplify. Assume that variables represent positive values.
328)
7 – 10
7 + 10
328)
A)
39 – 14 10
59
B)
1
C)
59 – 14 10
39
D)
59 + 14 10
39
Solve.
329)
4 x =9x + 9
329)
A)
9
25
B)
–9
5
C)
–9
8
D)
9
7
Write the following as a single radical. Assume that all variables represent nonnegative values.
330)
8x
330)
A)
4x
B)
8x
C)
10 x
D)
16 x
Find all square roots of the number.
331)
2116
331)
A)
±92
B)
±47
C)
±48
D)
±46
Find the quotient and write the answer in simplest form. Assume variables represent nonnegative values.
332)
21 375w5z12
3 3wz5
332)
A)
35w4z35z
B)
35w2z35w
C)
35w2z35z
D)
35w2z65z
38
Divide and write in standard form.
333)
4– 6i
5– 3i
333)
A)
19
17 – 9
17 i
B)
1
8+ 9
16 i
C)
2
17 + 42
17 i
D)
19
16 + 9
16 i
Rationalize the numerator. Assume that variables represent positive values.
334)
6 + 5
2
334)
A)
19
12 – 6 5
B)
31
12 – 2 5
C)
31
12 – 6 5
D)
19
12 – 2 5
Rewrite the following using radicals; then simplify if possible.
335)
9
25 1/2
335)
A)
9
25 =3
5
B)
9
25 =5
3
C)
9
25 =1
3
D)
9
25 =9
25
Simplify. Assume variables represent nonnegative values.
336)
54x2y
336)
A)
3xy 6
B)
3x 6y
C)
3x26y
D)
3xy26
Solve.
337)
2x + 15 – x = 6
337)
A)
–7, –3
B)
–3
C)
–7
D)
No solution
Use the rules of exponents to simplify. Write the answer with positive exponents. Assume that all variables represent
positive values.
338)
z-2/5·z3/5
338)
A)
z6/5
B)
z-1/5
C)
z1/5
D)
z5/6
Divide and write in standard form.
339)
9 – i
9i
339)
A)
1
9– i
B)
1
9+ i
C)
–1
9+ i
D)
–1
9– i
Write the following in exponential form. Assume that all variables represent positive values.
340)
1
733
340)
A)
3-7/3
B)
3-3/7
C)
37/3
D)
33/7
Add or subtract. Assume that variables represent nonnegative values.
341)
32 – 2 162– 10 72
341)
A)
-74 2
B)
-162 2
C)
74 2
D)
98 2
39
Evaluate the root, if possible.
342)
4–625
342)
A)
–25
B)
–5
C)
5
D)
Not real
Use the distributive property. Assume that variables represent nonnegative values.
343)
7(3 +7)
343)
A)
7 7 +3
B)
3 7 +7
C)
3 7 –7
D)
4 7
Solve. First isolate the radical term.
344)
x+2= 0
344)
A)
-4
B)
No solution
C)
4
D)
2
Simplify. Assume that variables represent positive values.
345)
33
s9
345)
A)
33
s4
B)
33
s
C)
3
s3
D)
33
s3
Find the root. Assume that variables represent nonnegative values.
346)
6a24b18
346)
A)
a18b24
B)
a4b3
C)
a3b4
D)
a24b18
Write the imaginary number using i.
347)
–16
347)
A)
–i 4
B)
4i
C)
±4
D)
–4i
Use a calculator to approximate the root to the nearest thousandth.
348)
359
348)
A)
3.893
B)
58.996
C)
3.897
D)
59.009
40
Answer Key
Testname: C8
1)
B
2)
D
3)
C
4)
Answers many vary. One possibility: Odd powers of negative numbers are negative, hence negative numbers can have
odd roots.
5)
x2– y
6)
No. When n is an odd positive integer, nxn= x, as in 3(-5)3= –5, but when n is an even positive integer,
nxn = x, as in 4(-5)4 = -5 = 5. (Explanations will vary.)
7)
The exponent was not applied to the numerical coefficient.
8)
Mistake: You cannot take the square root of a number, using the radical symbol, and obtain a negative number as the
result.
Correct: There is no solution.
9)
s =Sl*L
L; 66.1 mph
10)
Mistake: Divided the radicands without evaluating the root
Correct: 2
11)
Mistake: Squared 4 in the radicand
Correct: 45
12)
Each radical represents a whole number.
13)
One
14)
Mistake: Divided instead of evaluating the square root
Correct: 2
15)
False. The quotient rule for radicals also includes the stipulation that na and nb are both real numbers. If n is even
and a (or b) is negative, then na (or nb) is not real and the quotient rule for radicals does not apply.
16)
No.
17)
Mistake: Multiplied by 11 instead of 11
Correct: 33
11
18)
Indexes must be the same to combine terms.
19)
The statement is false. Let n = a = b = 1; 1 + 1 2. (Examples will vary.)
20)
T =2L
4; 7.30 ft
21)
Answers may vary. One possibility: First, satisfy the power in the denominator of the exponent by taking the cube root.
Then, multiply the result by the power in the numerator of the exponent.
22)
The statement is false. The correct answer is 3x2. It is obtained by applying the product rule for radicals. The answer
would be x if you were multiplying square roots, not cube roots. (Explanations will vary.)
23)
Answers will vary. One possibility: 3-13 =3–1 ·13 =3-1 ·313 = –313.
24)
Two
25)
The statement is false. The correct answer is x.
4x·4x=4x2 by the product rule for radicals.
Then4x2=x2/4 =x1/2 =x. (Explanations will vary.)
26)
A
41
Answer Key
Testname: C8
Answer Key
Testname: C8
43
Answer Key
Testname: C8
Answer Key
Testname: C8
45
Answer Key
Testname: C8
46
Answer Key
Testname: C8
47
Answer Key
Testname: C8
48