Download Chapter 9 — Answers

Math 154 ::
Elementary Algebra
Chapter 9 — Answers
Section 9.1
Section 9.2
Section 9.3
Section 9.4
Section 9.5
Section 9.6
Chapter 9 — Answers
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Math 154 :: Elementary Algebra
Section 9.1
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Chapter 9 — Answers
Introduction to Square Roots
This answer should be in your own words.
This answer should be in your own words.
No, the square root of a negative number does NOT have a real number value.
The expression under the square root sign is called the radicand.
6
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12
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10
0
not a real number
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9
 83
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15
not a real number
20
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22. a)
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16
x
4
9
 x (The negative sign in front of the x makes the negative x-value positive.)
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x
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7
1
300
Section 9.1 — Answers
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Math 154 :: Elementary Algebra
Section 9.2
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Chapter 9 — Answers
Simplifying Radical Expressions — Part I
This answer should be in your own words.
When factors are “pulled out from a square root”, multiplication is between those factors and the factors that remain under the
square root.
If the radicand in a square root expression has a variable raised to an exponent, the short cut rule for simplifying the square root
for that variable is to divide the exponent by 2.
This answer should be in your own words.
a) True
b) True
c) False
d) False
e) True
f) True
g) False
h) True
i) False
When multiplying two single-term square root expressions, it’s “easiest” to write the expression under one radical sign first.
Assuming all variables are nonnegative, the simplified answer for a problem that “squares a square root” or “square roots a
square” is the radicand. In other words, “squaring” and “square rooting” are inverses.
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3 2
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10 2
not a real number
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4 7
15 7
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6 11
10 3
20 7
21 6
x x
z5 z
k4 k
n200
p 200 p
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y2 5
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2a 4 2
4m8
7c6 d 4 2d
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8 p3q 4 3q
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8a10c8 d 5c
18v10u16 2v
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5a75 6
6 y12 z 5 3 y
2n4 2m
7 x25 y 21 10 z
Section 9.2 —Answers
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Math 154 :: Elementary Algebra
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6c18 d12 15d
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3a 4 10
9z 4 2z
10m2 n2 6
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5a 2 c3 14
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25w6
11k 5
3a9b
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15m2
16c2 d 2
Chapter 9 — Answers
7 10
42
3x 2
5y 2y
4xy3 yz
24 p6 q 4 2
36x18
14y 3 z
Section 9.2 —Answers
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Math 154 :: Elementary Algebra
Section 9.3
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Chapter 9 — Answers
Addition, Subtraction, and Multiplication of Radical Expressions
Only add square root expressions that have like-radicands. The explanation should be in your own words.
This answer should be in your own words.
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5 11
5 10
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13 5  3 6
6 3  7 2
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5 3
10  2 11
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40 3 12 5
9 6
11  3 2
15 12 3
12  5 11
39 2  34
5 22
13 7  13 5
2 10 12
9 11  22
18 5  12
32 3  48
x2  x 6
y2  y y
6a a  2a 2
15  4 5
6 14  42
40 11  165
12 7  20 42
6 5  20 2
72 21 12 14
8x  1 3 x
9a a  9a
1 6z z  1 6z2
5c 5c  5c 5
1 4n  1 4n 7n
18  6 5  3 2  10
8  8 7  3  21
40  4 3 10 6  3 2
57  16 2
Section 9.3 — Answers
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Math 154 :: Elementary Algebra
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21  8 14
40  20 5  12 2  6 10
36  91 3
62  114 3
82  21 14
26  8 10
42 3
3x 2  7 x x  2 x
y2  2 y z  z
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2n2  9n 3n  1 2n
11
22
w2  6 4w
8a  1 6a2
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z2
This answer should be in your own words.
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Chapter 9 — Answers
Section 9.3 — Answers
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Math 154 :: Elementary Algebra
Section 9.4
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Chapter 9 — Answers
Division of Radical Expressions
When simplifying a square root whose radicand is a quotient, usually it’s “easiest” to simplify/reduce the fraction first, before
taking the square root.
When simplifying an expression that consists of a quotient of square roots (without an addition or subtraction), simplify the
fraction first.
The three conditions that must be met in order for a square root expression to be considered “simplified” are:
a) No radicand can contain a factor that is a perfect square.
b) The radicand is not a quotient.
c) There are no radicals in the denominator.
This answer should be in your own words.
Expressions that require rationalizing the denominator are expressions with a single radical term in the denominator and
expressions with two terms (at least one of which has a radical term). The next part of the answer should be in your own words.
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z 4 13 z
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Section 9.4 — Answers
Caspers
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Math 154 :: Elementary Algebra
36.
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x2
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3c6 2c
8d 3
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2xy
xy 4
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Chapter 9 — Answers

2 1 6
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5
2 3 5

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4 10 3 2
7
2 3
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
x 8 x
8 5


64  x

11 11  y

11 y
2 a


a c
a c
xy x  y


x2  y
Section 9.4 — Answers
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Math 154 :: Elementary Algebra
Section 9.5
1.
2.
Chapter 9 — Answers
Simplifying Radical Expressions — Part II
This answer should be in your own words.
This answer should be in your own words.
4.
 3 5
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3  10
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 5 2 1
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75 2
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 4 1 1
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2 1 0
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1
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Section 9.5 — Answers
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Math 154 :: Elementary Algebra
Section 9.6
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b)
Chapter 9 — Answers
Radical Equations
4x 2
4x
x2  4 x  4
d) x  4 x  4
The first part of this answer should be in your own words. The inverse of square rooting is squaring.
It is necessary to check your answers when solving a square root equation. The rest of this answer should be in your own words.
x  64
y  16
a  81
m  100
w8
p9
no solution; 12 is an extraneous solution.
n  22
q  106
k  41
w  12
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d  3
y  11
x4
k 4
no solution
a2
p 1
n  3
no solution;  32 is an extraneous solution.
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x  1 6 ; 9 is an extraneous solution.
k   4 ; –7 is an extraneous solution.
w  5 ; –4 is an extraneous solution.
y   4 ; –9 is an extraneous solution.
z  3 ; 0 is an extraneous solution.
a  9 ; 1 is an extraneous solution.
c  4 ;  89 is an extraneous solution.
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m
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no solution;  1 are extraneous solutions.
x  3 ; 11 is an extraneous solution.
1
2
and m  7
Section 9.6 — Answers
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