Solve the problem.
99)
The length of the diagonal of a box is given by D =L2+W2+H2 where L, W, and H are the
length, width, and height of the box. Find the length of the diagonal, D, of a box that is 3 ft long, 6 ft
high, and 2 ft wide. Give the exact value.
99)
A)
7 ft
B)
11 ft
C)
6 ft
D)
36 ft
Provide an appropriate response.
100)
True or false? i3= – i
100)
A)
True
B)
False
Find the root if it is a real number.
101)
–
4625
101)
A)
–25
B)
–4
C)
Not a real number
D)
–5
Simplify. Assume that all variables represent positive real numbers.
102)
732– 3 354
102)
A)
232
B)
–232
C)
432
D)
732– 3 354
Express the radical in simplified form. Assume that all variables represent positive real numbers.
103)
–125k7q8
103)
A)
–5k3q45k
B)
5k7q85k
C)
5k3q45k
D)
–5k3q45
Simplify the radical. Assume that all variables represent positive real numbers.
104)
3256x4
4x
104)
A)
4x 34
B)
4x
C)
x364
D)
4x 3x
Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all
variables represent positive real numbers.
105)
y9/8
y5/8
105)
A)
1
y
B)
y1/2
C)
y
D)
y9/8
Solve the problem.
106)
In an economics study, three quantities m, p, and q have been found to be related by the equation
m =p1/2 ·q1/2. Find m, if p =4 and q =36.
106)
A)
12
B)
8
C)
72
D)
144
Write with rational exponents and then apply the properties of exponents. Assume that all radicands represent positive
real numbers. Give answers in exponential form.
107)
46w
107)
A)
w24
B)
w1/24
C)
1
w24
D)
24w
Rationalize the numerator. Assume that all variables represent positive real numbers.
108)
7+6
4
108)
A)
43
28 –4 6
B)
43
28 –7 6
C)
29
28 –4 6
D)
29
28 –7 6
Solve the equation.
109)
3x + 10 = 5 – 2x
109)
A)
5
4, 9
B)
{5}
C)
3
4
D)
3
4, 5
Simplify the radical. Assume that all variables represent positive real numbers.
110)
4625
1296
110)
A)
25
36
B)
5
6
C)
625
1296
D)
125
216
Solve the equation.
111)
4 x =9x + 9
111)
A)
–9
5
B)
–9
8
C)
9
7
D)
9
25
23
Write the expression in lowest terms. Assume that all variables represent positive real numbers.
112)
42 –24 14
30
112)
A)
7–414
5
B)
21 –12 7
15
C)
42 –8 7
5
D)
14 –24 14
5
Find the root if it is a real number.
113)
5
–32
113)
A)
–2
B)
10
C)
–10
D)
2
Simplify the root.
114)
–x10
114)
A)
– x5
B)
–x5
C)
x5
D)
–x5
Simplify. Assume that all variables represent positive real numbers.
115)
5x –x
5
115)
A)
0
B)
–1
5
C)
5x
5
D)
4 5x
5
Write the expression in the form a +
bi.
116)
9
4– 3i
116)
A)
36
7+27
7i
B)
36
7–27
7i
C)
36
25 –27
25 i
D)
36
25 +27
25 i
Find the decimal approximation for the radical. Round the answer to three decimal places.
117)
222
117)
A)
14.900
B)
14.897
C)
222.000
D)
14.905
Express the radical in simplified form.
118)
108
118)
A)
6
B)
6 3
C)
10
D)
36 3
Find the power of i.
119)
i4
119)
A)
i
B)
–i
C)
–1
D)
1
Multiply using the product rule.
120)
45·
425
120)
A)
5
B)
4125
C)
430
D)
830
Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all
variables represent positive real numbers.
121)
x2
y–4
1/2
121)
A)
x
y2
B)
xy1/2
C)
xy
D)
xy2
Simplify the expression involving rational exponents.
122)
271/3
122)
A)
243
B)
9
C)
81
D)
3
Find the equation of a circle satisfying the given conditions.
123)
Center: (0, –10); radius: 6
123)
A)
(x – 10)2+ y2=36
B)
x2+ (y – 10)2=6
C)
(x + 10)2+ y2=36
D)
x2+ (y + 10)2=36
Solve the problem.
124)
The following table gives data on two different solar modules being developed for use in roofing.
Model Watts Volts Amps Size (in inches) Cost (in dollars)
ABC–01 78 17.1 4.48 44 ×18 505
ABC–02 84 17.6 4.76 44 ×26 495
You must determine the size of the frame needed to support each panel on a roof. (Note: The sides
of each frame will form a right triangle, and the hypotenuse of the triangle will be the width of the
panel.) Use the Pythagorean theorem to find the dimensions of the legs for each frame if the legs
have equal length. Round your answers to the nearest tenth when necessary.
124)
A)
ABC–01: 3 in.;
ABC–02: 3.6 in.
B)
ABC–01: 9 in.;
ABC–02: 13 in.
C)
ABC–01: 12.7 in.;
ABC–02: 18.4 in.
D)
ABC–01: 4.5 in.;
ABC–02: 6.5 in.
Write with radicals. Assume that all variables represent positive real numbers.
125)
(9m + n) 5/6
125)
A)
59m + n6
B)
5(9m + n)6
C)
69m + n5
D)
6(9m + n)5
Find the power of i.
126)
i19
126)
A)
–1
B)
1
C)
i
D)
–i
Solve the problem.
127)
A manufacturer’s cost is given by C =5003n+ 1100, where C is the cost and n is the number of
parts produced. Find the cost when 216 parts are produced.
127)
A)
$8450
B)
$83
C)
$4100
D)
$2600
27
Multiply.
128)
(4 – 5i)2
128)
A)
16 – 15i
B)
16 – 65i
C)
41 – 40i
D)
–9– 40i
Solve the problem.
129)
The following table gives data on two different solar modules being developed for use in roofing.
Model Watts Volts Amps Size (in inches) Cost (in dollars)
ABC–01 72 16.8 3.8 44 ×20 475
ABC–02 68 17.3 4.21 44 ×16 480
You must determine the size of the frame needed to support each panel on a roof. (Note: The sides
of each frame will form a right triangle, and the hypotenuse of the triangle will be the width of the
panel.) Use the Pythagorean theorem to find the dimensions of the legs for each frame if one leg is
twice the length of the other. Round your answers to the nearest tenth when necessary.
129)
A)
ABC–01: 11.5 in. by 23.1 in.
ABC–02: 9.2 in. by 18.5 in.
B)
ABC–01: 2 in. by 4 in.
ABC–02: 1.8 in. by 3.6 in.
C)
ABC–01: 2.6 in. by 5.2 in.
ABC–02: 2.3 in. by 4.6 in.
D)
ABC–01: 8.9 in. by 17.9 in.
ABC–02: 7.2 in. by 14.3 in.
Find the square of the radical expression.
130)
–16
130)
A)
–4
B)
–16
C)
16
D)
4
Simplify the radical. Assume that all variables represent positive real numbers.
131)
5r4
243
131)
A)
5r4
3
B)
5r
3
C)
r
3
D)
5r4
243
Simplify the expression. Assume that all variables represent positive real numbers.
132)
x–6y–4
x–3y7
–3/7
132)
A)
x9/7y33/7
B)
x27/7y33/7
C)
x9/7y12
D)
x54/7y33/7
Solve the problem. Give the answer as a simplified radical expression.
133)
Find the perimeter of a lot with sides measuring 2 8, 518, 332, and 475 yards.
133)
A)
51 2 yards
B)
31 2+ 20 3 yards
C)
31 + 20 3 yards
D)
62 + 20 3 yards
Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all
variables represent positive real numbers.
134)
8x8/5(x11/5 – 8x)
134)
A)
8x19/5 –64
x13/5
B)
8
x19/5 –64
x13/5
C)
8
x19/5 – 64x13/5
D)
8x19/5 – 64x13/5
Simplify the expression involving rational exponents.
135)
1331
64
–2/3
135)
A)
121
16
B)
16
121
C)
64
1331
D)
1331
64
Solve the problem. Give the answer as a simplified radical expression.
136)
A rectangular coal bin has a length of 48 feet and a width of 48 feet. What is its perimeter?
136)
A)
8 4 feet
B)
16 3 feet
C)
16 4 feet
D)
8 3 feet
Simplify. Assume that all variables represent positive real numbers.
137)
125k7q8
137)
A)
5k2q45k
B)
5k3q45k
C)
5k7q85k
D)
5k3q45
Write with radicals. Assume that all variables represent positive real numbers.
138)
(5py2)1/3
138)
A)
55py
B)
35py
C)
35py2
D)
5py2
Solve the equation.
139)
x + 6 +2 – x = 4
139)
A)
{31, –2}
B)
{–2}
C)
{0}
D)
{2, –2}
Express the radical in simplified form.
140)
3
–729
140)
A)
–81
B)
9
C)
–9
D)
81
Add or subtract as indicated. Write your answer in the form a +
bi.
141)
(–8+ 7i) – 3
141)
A)
–11 + 7i
B)
–5+ 7i
C)
11 – 7i
D)
–5– 7i
Multiply or divide as indicated.
142)
–100 · – 16
142)
A)
–40i
B)
–40
C)
40
D)
40i
B
Find the equation of a circle satisfying the given conditions.
143)
Center: (0, –6); radius: 6
143)
A)
(x + 6)2+ y2=36
B)
x2+ (y + 6)2=6
C)
(x – 6)2+ y2=36
D)
x2+ (y – 6)2=6
B
Write the expression in the form a +
bi.
144)
5+ i
–4–8i
144)
A)
9
20 i
B)
–7
20 +9
20 i
C)
–7
20 –9
20 i
D)
–7
20
B
Find the distance between the pair of points.
145)
(2 2, 2 11) and (9 2, –211)
145)
A)
220
B)
255
C)
274
D)
274
D
A
Simplify the expression involving rational exponents.
146)
(–27)1/3
146)
A)
Not a real number
B)
–27
C)
–3
D)
3
Find all square roots of the number.
147)
196
9
147)
A)
49
2, –49
2
B)
7
2, –7
2
C)
14
3, –14
3
D)
5, –5
C
Evaluate.
148)
3
–27
148)
A)
–9
B)
3
C)
9
D)
–3
D
Rationalize the numerator. Assume that all variables represent positive real numbers.
149)
10 –3
7
149)
A)
103
70 +10 3
B)
97
70 +7 3
C)
–1
70 +10 3
D)
–1
70 +7 3
B
C
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.
150)
16
150)
A)
Rational, 4
B)
Not a real number
C)
Rational, 8.000
D)
Irrational, 8.000
Simplify the root.
151)
4x4
151)
A)
x
B)
–x
C)
|x|
D)
–x
Solve the equation.
152)
2k + 1 =7
152)
A)
{12}
B)
{48}
C)
{–24}
D)
{24}
Provide an appropriate response.
153)
True or false? If a > 0, then a
i= ia.
153)
A)
True
B)
False
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.
154)
–121
154)
A)
Not a real number
B)
Irrational, –60.500
C)
Rational, –11
D)
Irrational, –11.000
Write the expression in the form a +
bi.
155)
–2i
3– 8i
155)
A)
–16
73 –6
73 i
B)
16
55 +6
55 i
C)
–16
55 +6
55 i
D)
16
73 –6
73 i
Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all
variables represent positive real numbers.
156)
x1/3·x2/3
156)
A)
x2/3
B)
1
x
C)
x2/9
D)
x
Simplify the radical. Assume that all variables represent positive real numbers.
157)
4 2y7
32y3
157)
A)
y
2
B)
2y
C)
y2
4
D)
y
48
Simplify the expression. Assume that all variables represent positive real numbers.
158)
25
9
–3/2
158)
A)
125
27
B)
27
125
C)
25
9
D)
9
25