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Math Problems
Algebra 2
Simplify radical expressions involving fractions
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04082024
04082024
04082024
Homew
\newline
amihq.com/web/viewer. html?state
=
%
7
B
n
=\% 7 \mathrm{~B}^{\mathrm{n}}
=
%7
B
n
ids \(
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(
25
0
2
)
−
(
23
0
2
)
\sqrt{(250^2)-(230^2)}
(
25
0
2
)
−
(
23
0
2
)
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lim
x
→
∞
2
x
2
−
13
x
+
1
3
e
19
x
+
2
x
\lim _{x \rightarrow \infty} \frac{2 x^{2}-13 x+1}{3 e^{19 x}+2 x}
lim
x
→
∞
3
e
19
x
+
2
x
2
x
2
−
13
x
+
1
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2
x
−
14
=
288
x
2 \sqrt{x}-14=\frac{288}{\sqrt{x}}
2
x
−
14
=
x
288
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7
=
2
x
0.50
−
x
\sqrt{7}=\frac{2 x}{0.50-x}
7
=
0.50
−
x
2
x
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alves.
\newline
3
x
2
+
6
x
9
x
2
\frac{3 x^{2}+6 x}{9 x^{2}}
9
x
2
3
x
2
+
6
x
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cos
2
x
sin
3
x
−
sin
x
−
1
\frac{\cos 2x}{\sin 3x - \sin x} - 1
s
i
n
3
x
−
s
i
n
x
c
o
s
2
x
−
1
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2
18
+
x
2
x
\frac{2 \sqrt{18}+\sqrt{x}}{\sqrt{2 x}}
2
x
2
18
+
x
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5885
=
?
\sqrt{5885}=?
5885
=
?
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3
6
36
1
8
36
\frac{36^{36}}{18^{36}}
1
8
36
3
6
36
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2
2
×
225
2^{2} \times \sqrt{225}
2
2
×
225
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2
x
−
6
=
3
2
(
6
)
2 x-6=3^{2}(\sqrt{6})
2
x
−
6
=
3
2
(
6
)
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−
5
+
3
75
-5 + \frac{3}{75}
−
5
+
75
3
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−
4
5
/
2
-4^{5 / 2}
−
4
5/2
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6
14
−
42
24
\frac{6\sqrt{14} - \sqrt{42}}{24}
24
6
14
−
42
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(I)
lim
x
→
4
3
x
3
−
192
x
−
2
\lim _{x \rightarrow 4} \frac{3 x^{3}-192}{\sqrt{x}-2}
lim
x
→
4
x
−
2
3
x
3
−
192
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Divide using the standard algorithm.
\newline
3
,
543
/
34
3,543 / 34
3
,
543/34
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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
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
70
9
\sqrt{\frac{70}{9}}
9
70
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Simplify.
\newline
25
49
\sqrt{\frac{25}{49}}
49
25
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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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