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Math Problems
Algebra 2
Properties of operations on rational and irrational numbers
The number
s
s
s
is rational. Which statement about
2
+
s
2 + s
2
+
s
is true?
\newline
Choices:
\newline
(A)
2
+
s
2 + s
2
+
s
is rational.
\newline
(B)
2
+
s
2 + s
2
+
s
is irrational.
\newline
(C)
2
+
s
2 + s
2
+
s
can be rational or irrational, depending on the value of
s
s
s
.
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The number
w
w
w
is irrational. Which statement about
w
−
5
w - \sqrt{5}
w
−
5
is true?
\newline
Choices:
\newline
(A)
w
−
5
w - \sqrt{5}
w
−
5
is rational.
\newline
(B)
w
−
5
w - \sqrt{5}
w
−
5
is irrational.
\newline
(C)
w
−
5
w - \sqrt{5}
w
−
5
can be rational or irrational, depending on the value of
w
w
w
.
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The number
y
y
y
is rational.
e
e
e
is the base of the natural logarithm. Which statement about
y
−
e
y - e
y
−
e
is true?
\newline
Choices:
\newline
(A)
y
−
e
y - e
y
−
e
is rational.
\newline
(B)
y
−
e
y - e
y
−
e
is irrational.
\newline
(C)
y
−
e
y - e
y
−
e
can be rational or irrational, depending on the value of
y
y
y
.
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The number
c
c
c
is irrational.
e
e
e
is the base of the natural logarithm. Which statement about
c
−
e
c - e
c
−
e
is true?
\newline
Choices:
\newline
(A)
c
−
e
c - e
c
−
e
is rational.
\newline
(B)
c
−
e
c - e
c
−
e
is irrational.
\newline
(C)
c
−
e
c - e
c
−
e
can be rational or irrational, depending on the value of
c
c
c
.
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The number
t
t
t
is irrational. Which statement about
9
−
t
9 - t
9
−
t
is true?
\newline
Choices:
\newline
(A)
9
−
t
9 - t
9
−
t
is rational.
\newline
(B)
9
−
t
9 - t
9
−
t
is irrational.
\newline
(C)
9
−
t
9 - t
9
−
t
can be rational or irrational, depending on the value of
t
t
t
.
Get tutor help
The number
p
p
p
is rational.
e
e
e
is the base of the natural logarithm. Which statement about
p
+
e
p + e
p
+
e
is true?
\newline
Choices:
\newline
(A)
p
+
e
p + e
p
+
e
is rational.
\newline
(B)
p
+
e
p + e
p
+
e
is irrational.
\newline
(C)
p
+
e
p + e
p
+
e
can be rational or irrational, depending on the value of
p
p
p
.
Get tutor help
The number
q
q
q
is rational. Which statement about
q
+
2
q + 2
q
+
2
is true?
\newline
Choices:
\newline
(A)
q
+
2
q + 2
q
+
2
is rational.
\newline
(B)
q
+
2
q + 2
q
+
2
is irrational.
\newline
(C)
q
+
2
q + 2
q
+
2
can be rational or irrational, depending on the value of
q
q
q
.
Get tutor help
The number
u
u
u
is irrational. Which statement about
3
−
u
\sqrt{3} - u
3
−
u
is true?
\newline
Choices:
\newline
(A)
3
−
u
\sqrt{3} - u
3
−
u
is rational.
\newline
(B)
3
−
u
\sqrt{3} - u
3
−
u
is irrational.
\newline
(C)
3
−
u
\sqrt{3} - u
3
−
u
can be rational or irrational, depending on the value of
u
u
u
.
Get tutor help
The number
p
p
p
is irrational. Which statement about
p
−
8
p - 8
p
−
8
is true?
\newline
Choices:
\newline
(A)
p
−
8
p - 8
p
−
8
is rational.
\newline
(B)
p
−
8
p - 8
p
−
8
is irrational.
\newline
(C)
p
−
8
p - 8
p
−
8
can be rational or irrational, depending on the value of
p
p
p
.
Get tutor help
The number
z
z
z
is irrational. Which statement about
9
+
z
9 + z
9
+
z
is true?
\newline
Choices:
\newline
(A)
9
+
z
9 + z
9
+
z
is rational.
\newline
(B)
9
+
z
9 + z
9
+
z
is irrational.
\newline
(C)
9
+
z
9 + z
9
+
z
can be rational or irrational, depending on the value of
z
z
z
.
Get tutor help
The number
b
b
b
is irrational. Which statement about
b
−
9
b - 9
b
−
9
is true?
\newline
Choices:
\newline
(A)
b
−
9
b - 9
b
−
9
is rational.
\newline
(B)
b
−
9
b - 9
b
−
9
is irrational.
\newline
(C)
b
−
9
b - 9
b
−
9
can be rational or irrational, depending on the value of
b
b
b
.
Get tutor help
The number
y
y
y
is rational. Which statement about
35
+
y
\sqrt{35} + y
35
+
y
is true?
\newline
Choices:
\newline
(A)
35
+
y
\sqrt{35} + y
35
+
y
is rational.
\newline
(B)
35
+
y
\sqrt{35} + y
35
+
y
is irrational.
\newline
(C)
35
+
y
\sqrt{35} + y
35
+
y
can be rational or irrational, depending on the value of
y
y
y
.
Get tutor help
The number
x
x
x
is irrational. Which statement about
2
+
x
2 + x
2
+
x
is true?
\newline
Choices:
\newline
(A)
2
+
x
2 + x
2
+
x
is rational.
\newline
(B)
2
+
x
2 + x
2
+
x
is irrational.
\newline
(C)
2
+
x
2 + x
2
+
x
can be rational or irrational, depending on the value of
x
x
x
.
Get tutor help
The number
b
b
b
is rational. Which statement about
b
−
8
b - 8
b
−
8
is true?
\newline
Choices:
\newline
(A)
b
−
8
b - 8
b
−
8
is rational.
\newline
(B)
b
−
8
b - 8
b
−
8
is irrational.
\newline
(C)
b
−
8
b - 8
b
−
8
can be rational or irrational, depending on the value of
b
b
b
.
Get tutor help
The number
c
c
c
is rational. Which statement about
7
−
c
\sqrt{7} - c
7
−
c
is true?
\newline
Choices:
\newline
(A)
7
−
c
\sqrt{7} - c
7
−
c
is rational.
\newline
(B)
7
−
c
\sqrt{7} - c
7
−
c
is irrational.
\newline
(C)
7
−
c
\sqrt{7} - c
7
−
c
can be rational or irrational, depending on the value of
c
c
c
.
Get tutor help
The number
q
q
q
is irrational.
e
e
e
is the base of the natural logarithm. Which statement about
q
−
e
q - e
q
−
e
is true?
\newline
Choices:
\newline
(A)
q
−
e
q - e
q
−
e
is rational.
\newline
(B)
q
−
e
q - e
q
−
e
is irrational.
\newline
(C)
q
−
e
q - e
q
−
e
can be rational or irrational, depending on the value of
q
q
q
.
Get tutor help
The number
q
q
q
is rational. Which statement about
2
+
q
2 + q
2
+
q
is true?
\newline
Choices:
\newline
(A)
2
+
q
2 + q
2
+
q
is rational.
\newline
(B)
2
+
q
2 + q
2
+
q
is irrational.
\newline
(C)
2
+
q
2 + q
2
+
q
can be rational or irrational, depending on the value of
q
q
q
.
Get tutor help
is the base of the natural logarithm. The number
v
v
v
is irrational. Which statement about
−
v
- v
−
v
is true?
\newline
Choices:
\newline
(A)
−
v
- v
−
v
is rational.
\newline
(B)
−
v
- v
−
v
is irrational.
\newline
(C)
−
v
- v
−
v
can be rational or irrational, depending on the value of
v
v
v
.
Get tutor help
The number
u
u
u
is rational. Which statement about
2
−
u
2 - u
2
−
u
is true?
\newline
Choices:
\newline
(A)
2
−
u
2 - u
2
−
u
is rational.
\newline
(B)
2
−
u
2 - u
2
−
u
is irrational.
\newline
(C)
2
−
u
2 - u
2
−
u
can be rational or irrational, depending on the value of
u
u
u
.
Get tutor help
The number
w
w
w
is irrational. Which statement about
9
−
w
9 - w
9
−
w
is true?
\newline
Choices:
\newline
(A)
9
−
w
9 - w
9
−
w
is rational.
\newline
(B)
9
−
w
9 - w
9
−
w
is irrational.
\newline
(C)
9
−
w
9 - w
9
−
w
can be rational or irrational, depending on the value of
w
w
w
.
Get tutor help
The number
y
y
y
is irrational.
e
e
e
is the base of the natural logarithm. Which statement about
y
−
e
y - e
y
−
e
is true?
\newline
Choices:
\newline
(A)
y
−
e
y - e
y
−
e
is rational.
\newline
(B)
y
−
e
y - e
y
−
e
is irrational.
\newline
(C)
y
−
e
y - e
y
−
e
can be rational or irrational, depending on the value of
y
y
y
.
Get tutor help
The number
z
z
z
is rational. Which statement about
5
+
z
5 + z
5
+
z
is true?
\newline
Choices:
\newline
(A)
5
+
z
5 + z
5
+
z
is rational.
\newline
(B)
5
+
z
5 + z
5
+
z
is irrational.
\newline
(C)
5
+
z
5 + z
5
+
z
can be rational or irrational, depending on the value of
z
z
z
.
Get tutor help
is the base of the natural logarithm. The number
w
w
w
is irrational. Which statement about
e
+
w
e + w
e
+
w
is true?
\newline
Choices:
\newline
(A)
e
+
w
e + w
e
+
w
is rational.
\newline
(B)
e
+
w
e + w
e
+
w
is irrational.
\newline
(C)
e
+
w
e + w
e
+
w
can be rational or irrational, depending on the value of
w
w
w
.
Get tutor help
The number
x
x
x
is irrational. Which statement about
x
−
6
x - 6
x
−
6
is true?
\newline
Choices:
\newline
(A)
x
−
6
x - 6
x
−
6
is rational.
\newline
(B)
x
−
6
x - 6
x
−
6
is irrational.
\newline
(C)
x
−
6
x - 6
x
−
6
can be rational or irrational, depending on the value of
x
x
x
.
Get tutor help
The number
v
v
v
is rational. Which statement about
38
−
v
\sqrt{38} - v
38
−
v
is true?
\newline
Choices:
\newline
(A)
38
−
v
\sqrt{38} - v
38
−
v
is rational.
\newline
(B)
38
−
v
\sqrt{38} - v
38
−
v
is irrational.
\newline
(C)
38
−
v
\sqrt{38} - v
38
−
v
can be rational or irrational, depending on the value of
v
v
v
.
Get tutor help
The number
a
a
a
is irrational. Which statement about
a
+
5
a + 5
a
+
5
is true?
\newline
Choices:
\newline
(A)
a
+
5
a + 5
a
+
5
is rational.
\newline
(B)
a
+
5
a + 5
a
+
5
is irrational.
\newline
(C)
a
+
5
a + 5
a
+
5
can be rational or irrational, depending on the value of
a
a
a
.
Get tutor help
The number
q
q
q
is rational. Which statement about
q
−
8
q - 8
q
−
8
is true?
\newline
Choices:
\newline
(A)
q
−
8
q - 8
q
−
8
is rational.
\newline
(B)
q
−
8
q - 8
q
−
8
is irrational.
\newline
(C)
q
−
8
q - 8
q
−
8
can be rational or irrational, depending on the value of
q
q
q
.
Get tutor help
is the base of the natural logarithm. The number
s
s
s
is rational. Which statement about
e
+
s
e + s
e
+
s
is true?
\newline
Choices:
\newline
(A)
e
+
s
e + s
e
+
s
is rational.
\newline
(B)
e
+
s
e + s
e
+
s
is irrational.
\newline
(C)
e
+
s
e + s
e
+
s
can be rational or irrational, depending on the value of
s
s
s
.
Get tutor help
The number
w
w
w
is irrational. Which statement about
6
−
w
6 - w
6
−
w
is true?
\newline
Choices:
\newline
(A)
6
−
w
6 - w
6
−
w
is rational.
\newline
(B)
6
−
w
6 - w
6
−
w
is irrational.
\newline
(C)
6
−
w
6 - w
6
−
w
can be rational or irrational, depending on the value of
w
w
w
.
Get tutor help
The number
b
b
b
is rational. Which statement about
b
−
6
b - 6
b
−
6
is true?
\newline
Choices:
\newline
(A)
b
−
6
b - 6
b
−
6
is rational.
\newline
(B)
b
−
6
b - 6
b
−
6
is irrational.
\newline
(C)
b
−
6
b - 6
b
−
6
can be rational or irrational, depending on the value of
b
b
b
.
Get tutor help
The number
s
s
s
is irrational. Which statement about
s
+
4
s + 4
s
+
4
is true?
\newline
Choices:
\newline
(A)
s
+
4
s + 4
s
+
4
is rational.
\newline
(B)
s
+
4
s + 4
s
+
4
is irrational.
\newline
(C)
s
+
4
s + 4
s
+
4
can be rational or irrational, depending on the value of
s
s
s
.
Get tutor help
The number
u
u
u
is rational.
e
e
e
is the base of the natural logarithm. Which statement about
u
+
e
u + e
u
+
e
is true?
\newline
Choices:
\newline
(A)
u
+
e
u + e
u
+
e
is rational.
\newline
(B)
u
+
e
u + e
u
+
e
is irrational.
\newline
(C)
u
+
e
u + e
u
+
e
can be rational or irrational, depending on the value of
u
u
u
.
Get tutor help
The number
p
p
p
is irrational.
e
e
e
is the base of the natural logarithm. Which statement about
p
−
e
p - e
p
−
e
is true?
\newline
Choices:
\newline
(A)
p
−
e
p - e
p
−
e
is rational.
\newline
(B)
p
−
e
p - e
p
−
e
is irrational.
\newline
(C)
p
−
e
p - e
p
−
e
can be rational or irrational, depending on the value of
p
p
p
.
Get tutor help
The number
t
t
t
is irrational. Which statement about
t
−
π
t - \pi
t
−
π
is true?
\newline
Choices:
\newline
(A)
t
−
π
t - \pi
t
−
π
is rational.
\newline
(B)
t
−
π
t - \pi
t
−
π
is irrational.
\newline
(C)
t
−
π
t - \pi
t
−
π
can be rational or irrational, depending on the value of
t
t
t
.
Get tutor help
The number
s
s
s
is rational. Which statement about
s
+
π
s + \pi
s
+
π
is true?
\newline
Choices:
\newline
(A)
s
+
π
s + \pi
s
+
π
is rational.
\newline
(B)
s
+
π
s + \pi
s
+
π
is irrational.
\newline
(C)
s
+
π
s + \pi
s
+
π
can be rational or irrational, depending on the value of
s
s
s
.
Get tutor help
The number
a
a
a
is irrational. Which statement about
a
−
12
a - \sqrt{12}
a
−
12
is true?
\newline
Choices:
\newline
(A)
a
−
12
a - \sqrt{12}
a
−
12
is rational.
\newline
(B)
a
−
12
a - \sqrt{12}
a
−
12
is irrational.
\newline
(C)
a
−
12
a - \sqrt{12}
a
−
12
can be rational or irrational, depending on the value of
a
a
a
.
Get tutor help
The number
s
s
s
is irrational.
e
e
e
is the base of the natural logarithm. Which statement about
s
−
e
s - e
s
−
e
is true?
\newline
Choices:
\newline
(A)
s
−
e
s - e
s
−
e
is rational.
\newline
(B)
s
−
e
s - e
s
−
e
is irrational.
\newline
(C)
s
−
e
s - e
s
−
e
can be rational or irrational, depending on the value of
s
s
s
.
Get tutor help
The number
u
u
u
is irrational. Which statement about
45
+
u
\sqrt{45} + u
45
+
u
is true?
\newline
Choices:
\newline
(A)
45
+
u
\sqrt{45} + u
45
+
u
is rational.
\newline
(B)
45
+
u
\sqrt{45} + u
45
+
u
is irrational.
\newline
(C)
45
+
u
\sqrt{45} + u
45
+
u
can be rational or irrational, depending on the value of
u
u
u
.
Get tutor help
The number
u
u
u
is rational. Which statement about
5
+
u
5 + u
5
+
u
is true?
\newline
Choices:
\newline
(A)
5
+
u
5 + u
5
+
u
is rational.
\newline
(B)
5
+
u
5 + u
5
+
u
is irrational.
\newline
(C)
5
+
u
5 + u
5
+
u
can be rational or irrational, depending on the value of
u
u
u
.
Get tutor help
The number
r
r
r
is rational.
e
e
e
is the base of the natural logarithm. Which statement about
r
−
e
r - e
r
−
e
is true?
\newline
Choices:
\newline
(A)
r
−
e
r - e
r
−
e
is rational.
\newline
(B)
r
−
e
r - e
r
−
e
is irrational.
\newline
(C)
r
−
e
r - e
r
−
e
can be rational or irrational, depending on the value of
r
r
r
.
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The number
w
w
w
is irrational.
e
e
e
is the base of the natural logarithm. Which statement about
w
−
e
w - e
w
−
e
is true?
\newline
Choices:
\newline
(A)
w
−
e
w - e
w
−
e
is rational.
\newline
(B)
w
−
e
w - e
w
−
e
is irrational.
\newline
(C)
w
−
e
w - e
w
−
e
can be rational or irrational, depending on the value of
w
w
w
.
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The number
w
w
w
is irrational.
e
e
e
is the base of the natural logarithm. Which statement about
w
+
e
w + e
w
+
e
is true?
\newline
Choices:
\newline
(A)
w
+
e
w + e
w
+
e
is rational.
\newline
(B)
w
+
e
w + e
w
+
e
is irrational.
\newline
(C)
w
+
e
w + e
w
+
e
can be rational or irrational, depending on the value of
w
w
w
.
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The number
v
v
v
is rational. Which statement about
5
+
v
5 + v
5
+
v
is true?
\newline
Choices:
\newline
(A)
5
+
v
5 + v
5
+
v
is rational.
\newline
(B)
5
+
v
5 + v
5
+
v
is irrational.
\newline
(C)
5
+
v
5 + v
5
+
v
can be rational or irrational, depending on the value of
v
v
v
.
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The number
s
s
s
is rational. Which statement about
10
+
s
10 + s
10
+
s
is true?
\newline
Choices:
\newline
(A)
10
+
s
10 + s
10
+
s
is rational.
\newline
(B)
10
+
s
10 + s
10
+
s
is irrational.
\newline
(C)
10
+
s
10 + s
10
+
s
can be rational or irrational, depending on the value of
s
s
s
.
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The number
q
q
q
is irrational. Which statement about
q
−
4
q - 4
q
−
4
is true?
\newline
Choices:
\newline
(A)
q
−
4
q - 4
q
−
4
is rational.
\newline
(B)
q
−
4
q - 4
q
−
4
is irrational.
\newline
(C)
q
−
4
q - 4
q
−
4
can be rational or irrational, depending on the value of
q
q
q
.
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The number
a
a
a
is rational. Which statement about
a
−
3
a - 3
a
−
3
is true?
\newline
Choices:
\newline
(A)
a
−
3
a - 3
a
−
3
is rational.
\newline
(B)
a
−
3
a - 3
a
−
3
is irrational.
\newline
(C)
a
−
3
a - 3
a
−
3
can be rational or irrational, depending on the value of
a
a
a
.
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The number
z
z
z
is irrational. Which statement about
3
−
z
3 - z
3
−
z
is true?
\newline
Choices:
\newline
(A)
3
−
z
3 - z
3
−
z
is rational.
\newline
(B)
3
−
z
3 - z
3
−
z
is irrational.
\newline
(C)
3
−
z
3 - z
3
−
z
can be rational or irrational, depending on the value of
z
z
z
.
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The number
s
s
s
is irrrational. Which statement about
s
−
8
s - 8
s
−
8
is true? Choices:
\newline
(A)
s
−
8
s - 8
s
−
8
is rational.
\newline
(B)
s
+
8
s + 8
s
+
8
is irrational.
\newline
(C)
s
+
8
s + 8
s
+
8
can be rational or irrational, depending on the value of
s
s
s
.
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The number
p
p
p
is rational, and the number
q
q
q
is rational and positive. Which statement about
p
q
\frac{p}{q}
q
p
is true?
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The number
t
t
t
is rational. Which statement about
5
+
t
5 + t
5
+
t
is true?
\newline
Choices:
\newline
(A)
5
+
t
5 + t
5
+
t
is rational.
\newline
(B)
5
+
t
5 + t
5
+
t
is irrational.
\newline
(C)
5
+
t
5 + t
5
+
t
can be rational or irrational, depending on the value of
t
t
t
.
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