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Math Problems
Algebra 2
Simplify radical expressions involving fractions
3.5
3
p
3
+
7
4
p
\qquad \dfrac{3.5}{3p^3} + \dfrac{7}{4p}
3
p
3
3.5
+
4
p
7
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25
h
2
+
144
h
2
+
h
2
3
\sqrt{25h^2+144h^2}+\sqrt[3]{h^2}
25
h
2
+
144
h
2
+
3
h
2
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r
2
+
14
r
+
49
r
2
+
15
r
+
56
\frac{r^2+14r+49}{r^2+15r+56}
r
2
+
15
r
+
56
r
2
+
14
r
+
49
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Simplify:
\newline
4740
30
\frac{4740}{30}
30
4740
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Simplify:
(
0.0144
0.0289
)
\sqrt{\left(\frac{0.0144}{0.0289}\right)}
(
0.0289
0.0144
)
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1
8
×
3
−
3
\frac{1}{8}\times\frac{3}{-3}
8
1
×
−
3
3
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Solve for
x
x
x
:
4
3
x
×
4
6
=
1
4^{3x} \times 4^6 = 1
4
3
x
×
4
6
=
1
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(
4
u
2
v
4
)
4
\left(4 u^{2} v^{4}\right)^{4}
(
4
u
2
v
4
)
4
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Simplify.
\newline
10
d
3
5
d
\frac{10d^{3}}{5d}
5
d
10
d
3
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7
2
3
of
3
5
÷
3
1
5
−
2
11
7\frac{2}{3} \text{ of } \frac{3}{5}÷3\frac{1}{5}-\frac{2}{11}
7
3
2
of
5
3
÷
3
5
1
−
11
2
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min
w
∥
X
w
−
y
∥
2
2
\min _{w}\|X w-y\|_{2}^{2}
min
w
∥
Xw
−
y
∥
2
2
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Simplify:
\newline
(
x
+
1
)
(
x
−
4
)
\left(x + 1\right)\left(x - 4\right)
(
x
+
1
)
(
x
−
4
)
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Simplify.
\newline
9
11
\frac{9}{11}
11
9
−
1
-1
−
1
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(
x
6
/
5
)
5
\left(x^{6 / 5}\right)^{5}
(
x
6/5
)
5
=
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Solve for
n
n
n
.
\newline
n
100
(
1.5
−
n
)
100
\frac{\frac{n}{100}}{\frac{(1.5-n)}{100}}
100
(
1.5
−
n
)
100
n
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Write the expression in simplest form.
\newline
2
a
+
b
4
a
2
−
b
2
\frac{2 a+b}{4 a^{2}-b^{2}}
4
a
2
−
b
2
2
a
+
b
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11
n
=
8
5
\dfrac{11}{n} = \dfrac{8}{5}
n
11
=
5
8
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p
8
=
7
9
\dfrac{p}{8} = \dfrac{7}{9}
8
p
=
9
7
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k
6
=
4
3
\dfrac{k}{6} = \dfrac{4}{3}
6
k
=
3
4
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4
r
=
5
7
\dfrac{4}{r} = \dfrac{5}{7}
r
4
=
7
5
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n
8
=
11
5
\dfrac{n}{8} = \dfrac{11}{5}
8
n
=
5
11
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44
\sqrt{44}
44
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Simplify
\newline
(
5
+
3
)
(
5
−
3
)
22
\frac{(5+\sqrt{3})(5-\sqrt{3})}{\sqrt{22}}
22
(
5
+
3
)
(
5
−
3
)
\newline
Give your answer in its simplest form.
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Convert
145
8
\frac{145}{8}
8
145
into a rational number.
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Which expression is equivalent to
(
3
2
)
1
(3^2)^1
(
3
2
)
1
?
\newline
Choices:
\newline
(A)
1
3
3
\frac{1}{3^3}
3
3
1
\newline
(B)
3
2
3^2
3
2
\newline
(C)
3
3
3^3
3
3
\newline
(D)
1
3
2
\frac{1}{3^2}
3
2
1
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Which expression is equivalent to
6
×
6
3
6 \times 6^3
6
×
6
3
?
\newline
Choices:
\newline
(A)
1
6
4
\frac{1}{6^4}
6
4
1
\newline
(B)
1
6
3
\frac{1}{6^3}
6
3
1
\newline
(C)
6
4
6^4
6
4
\newline
(D)
6
3
6^3
6
3
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Which expression is equivalent to
1
1
9
×
1
1
2
11^9 \times 11^2
1
1
9
×
1
1
2
?
\newline
Choices:
\newline
(A)
1
1
1
11
\frac{1}{11^{11}}
1
1
11
1
\newline
(B)
1
1
18
11^{18}
1
1
18
\newline
(C)
1
1
11
11^{11}
1
1
11
\newline
(D)
1
1
1
18
\frac{1}{11^{18}}
1
1
18
1
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(*)
\newline
lim
x
→
∞
x
x
\lim _{x \rightarrow \infty} \frac{\sqrt{x}}{x}
x
→
∞
lim
x
x
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Differentiate
y
=
(
5
x
+
3
10
x
−
6
)
4
y=(\frac{5x+3}{10x-6})^4
y
=
(
10
x
−
6
5
x
+
3
)
4
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25
x
8
\sqrt{25 \sqrt{x^{8}}}
25
x
8
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r
s
5
r
2
s
5
r
s
−
15
r
3
s
r
135
s
2
\sqrt{r s} \sqrt{5 r^{2} s} \sqrt{5 r s}-\sqrt{15 r^{3} s} \sqrt{r} \sqrt{135 s^{2}}
rs
5
r
2
s
5
rs
−
15
r
3
s
r
135
s
2
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(
6
n
2
)
(
2
n
)
\left(6 n^{2}\right)(2 n)
(
6
n
2
)
(
2
n
)
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462.84
÷
8.12
4 6 2 . 8 4 \div 8 . 1 2
462.84
÷
8.12
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Simplify.
\newline
12
49
\sqrt{\frac{12}{49}}
49
12
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Simplify.
\newline
27
25
\sqrt{\frac{27}{25}}
25
27
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Simplify.
\newline
8
9
\sqrt{\frac{8}{9}}
9
8
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Simplify.
\newline
50
9
\sqrt{\frac{50}{9}}
9
50
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Simplify.
\newline
45
49
\sqrt{\frac{45}{49}}
49
45
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Simplify.
\newline
20
9
\sqrt{\frac{20}{9}}
9
20
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Simplify.
\newline
245
4
\sqrt{\frac{245}{4}}
4
245
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Simplify.
\newline
25
49
\sqrt{\frac{25}{49}}
49
25
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Simplify.
\newline
70
9
\sqrt{\frac{70}{9}}
9
70
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Simplify.
\newline
20
49
\sqrt{\frac{20}{49}}
49
20
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Simplify.
\newline
75
49
\sqrt{\frac{75}{49}}
49
75
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Simplify.
\newline
28
25
\sqrt{\frac{28}{25}}
25
28
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Simplify.
\newline
10
49
\sqrt{\frac{10}{49}}
49
10
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Simplify.
\newline
21
4
\sqrt{\frac{21}{4}}
4
21
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Simplify.
\newline
28
9
\sqrt{\frac{28}{9}}
9
28
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Simplify.
\newline
63
25
\sqrt{\frac{63}{25}}
25
63
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Simplify.
\newline
125
9
\sqrt{\frac{125}{9}}
9
125
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1
2
3
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