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Math Problems
Precalculus
Properties of operations on rational and irrational numbers
The number
a
a
a
is irrational. Which statement about
a
38
a^{38}
a
38
is true?
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The number
q
q
q
is irrational. Which statement about
q
+
18
q + \sqrt{18}
q
+
18
is true?
\newline
Choices:
\newline
(A)
q
+
18
q + \sqrt{18}
q
+
18
is rational.
\newline
(B)
q
+
18
q + \sqrt{18}
q
+
18
is irrational.
\newline
(C)
q
+
18
q + \sqrt{18}
q
+
18
can be rational or irrational, depending on the value of
q
q
q
.
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The number
b
b
b
is rational. Which statement about
44
−
b
\sqrt{44} - b
44
−
b
is true?
\newline
Choices:
\newline
(A)
44
−
b
\sqrt{44} - b
44
−
b
is rational.
\newline
(B)
44
−
b
\sqrt{44} - b
44
−
b
is irrational.
\newline
(C)
44
−
b
\sqrt{44} - b
44
−
b
can be rational or irrational, depending on the value of
b
b
b
.
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The number
v
v
v
is irrational. Which statement about
32
−
v
\sqrt{32} - v
32
−
v
is true?
\newline
Choices:
\newline
(A)
32
−
v
\sqrt{32} - v
32
−
v
is rational.
\newline
(B)
32
−
v
\sqrt{32} - v
32
−
v
is irrational.
\newline
(C)
32
−
v
\sqrt{32} - v
32
−
v
can be rational or irrational, depending on the value of
v
v
v
.
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The number
b
b
b
is irrational. Which statement about
6
−
b
6 - b
6
−
b
is true?
\newline
Choices:
\newline
(A)
6
−
b
6 - b
6
−
b
is rational.
\newline
(B)
6
−
b
6 - b
6
−
b
is irrational.
\newline
(C)
6
−
b
6 - b
6
−
b
can be rational or irrational, depending on the value of
b
b
b
.
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The number
b
b
b
is rational. Which statement about
π
+
b
\pi + b
π
+
b
is true?
\newline
Choices:
\newline
(A)
π
+
b
\pi + b
π
+
b
is rational.
\newline
(B)
π
+
b
\pi + b
π
+
b
is irrational.
\newline
(C)
π
+
b
\pi + b
π
+
b
can be rational or irrational, depending on the value of
b
b
b
.
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The number
d
d
d
is irrational. Which statement about
24
−
d
\sqrt{24} - d
24
−
d
is true?
\newline
Choices:
\newline
(A)
24
−
d
\sqrt{24} - d
24
−
d
is rational.
\newline
(B)
24
−
d
\sqrt{24} - d
24
−
d
is irrational.
\newline
(C)
24
−
d
\sqrt{24} - d
24
−
d
can be rational or irrational, depending on the value of
d
d
d
.
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