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Math Problems
Algebra 1
Simplify radical expressions with variables
Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
180
\sqrt{180}
180
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
12
\sqrt{12}
12
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
108
\sqrt{108}
108
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
63
\sqrt{63}
63
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
175
=
\sqrt{175}=
175
=
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
20
\sqrt{20}
20
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
75
=
\sqrt{75}=
75
=
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
18
\sqrt{18}
18
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
450
\sqrt{450}
450
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
50
\sqrt{50}
50
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
28
\sqrt{28}
28
=
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
72
\sqrt{72}
72
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Simplify.
\newline
Multiply and remove all perfect squares from inside the square roots. Assume
\newline
a
a
a
is positive.
\newline
2
a
⋅
14
a
3
⋅
5
a
=
\sqrt{2a}\cdot\sqrt{14a^{3}}\cdot\sqrt{5a}=
2
a
⋅
14
a
3
⋅
5
a
=
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Simplify.
\newline
Multiply and remove all perfect squares from inside the square roots. Assume
\newline
x
x
x
is positive.
\newline
2
7
x
⋅
3
14
x
2
=
2\sqrt{7x}\cdot3\sqrt{14x^{2}}=
2
7
x
⋅
3
14
x
2
=
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Simplify.
\newline
Remove all perfect squares from inside the square roots. Assume
\newline
y
y
y
and
\newline
z
z
z
are positive.
\newline
75
y
z
2
\sqrt{75 yz^{2}}
75
y
z
2
=
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Simplify.
\newline
Remove all perfect squares from inside the square root. Assume
\newline
a
a
a
is positive.
\newline
27
a
\sqrt{27 a}
27
a
=
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
52
x
4
=
\sqrt{52x^{4}}=
52
x
4
=
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Simplify.
\newline
Multiply and remove all perfect squares from inside the square roots. Assume
\newline
a
a
a
is positive.
\newline
3
5
a
×
8
35
a
2
=
3\sqrt{5a} \times 8\sqrt{35a^{2}}=
3
5
a
×
8
35
a
2
=
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Simplify.
\newline
Remove all perfect squares from inside the square root. Assume
\newline
x
x
x
is positive.
\newline
20
x
8
=
\sqrt{20x^{8}}=
20
x
8
=
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Simplify.
\newline
Multiply and remove all perfect squares from inside the square roots. Assume
\newline
y
y
y
is positive.
\newline
6
15
y
4
×
2
20
y
2
=
6\sqrt{15y^{4}}\times2\sqrt{20y^{2}}=
6
15
y
4
×
2
20
y
2
=
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Simplify.
\newline
Remove all perfect squares from inside the square root. Assume
\newline
z
z
z
is positive.
\newline
72
z
5
\sqrt{72z^{5}}
72
z
5
=
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Simplify.
\newline
Remove all perfect squares from inside the square roots. Assume
\newline
a
a
a
and
\newline
b
b
b
are positive.
\newline
81
a
5
b
\sqrt{81a^{5}b}
81
a
5
b
=
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Simplify.
\newline
Remove all perfect squares from inside the square roots. Assume
\newline
a
a
a
and
\newline
b
b
b
are positive.
\newline
42
a
4
b
6
\sqrt{42a^{4}b^{6}}
42
a
4
b
6
=
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Simplify.
\newline
Multiply and remove all perfect squares from inside the square roots. Assume
\newline
z
z
z
is positive.
\newline
5
14
z
2
⋅
4
21
z
3
=
5\sqrt{14z^{2}} \cdot 4\sqrt{21z^{3}} =
5
14
z
2
⋅
4
21
z
3
=
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Simplify. Remove all perfect squares from inside the square roots. Assume
x
x
x
and
y
y
y
are positive.
\newline
8
x
3
y
2
\sqrt{8x^{3}y^{2}}
8
x
3
y
2
=
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Simplify.
\newline
Remove all perfect squares from inside the square roots. Assume
\newline
x
x
x
and
\newline
z
z
z
are positive.
\newline
72
x
3
z
3
\sqrt{72x^{3}z^{3}}
72
x
3
z
3
=
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
30
b
5
\sqrt{30b^{5}}
30
b
5
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Simplify.
\newline
Remove all perfect squares from inside the square root. Assume
\newline
y
y
y
is positive.
\newline
39
y
9
=
\sqrt{39y^{9}}=
39
y
9
=
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Simplify.
\newline
Remove all perfect squares from inside the square root. Assume
\newline
x
x
x
is positive.
\newline
54
x
7
\sqrt{54x^{7}}
54
x
7
=
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Simplify.
\newline
Remove all perfect squares from inside the square root. Assume
\newline
b
b
b
is positive.
\newline
80
b
2
=
\sqrt{80b^{2}} =
80
b
2
=
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Simplify.
\newline
Remove all perfect squares from inside the square root. Assume
\newline
y
y
y
is positive.
\newline
200
y
4
=
\sqrt{200y^{4}} =
200
y
4
=
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Simplify.
\newline
Multiply and remove all perfect squares from inside the square roots. Assume
\newline
x
x
x
is positive.
\newline
3
x
4
⋅
5
x
2
⋅
10
\sqrt{3x^{4}}\cdot\sqrt{5x^{2}}\cdot\sqrt{10}
3
x
4
⋅
5
x
2
⋅
10
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Simplify.
\newline
Remove all perfect squares from inside the square root. Assume
\newline
a
a
a
is positive.
\newline
108
a
6
\sqrt{108a^{6}}
108
a
6
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
56
z
7
=
\sqrt{56z^{7}}=
56
z
7
=
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
15
y
3
=
\sqrt{15y^{3}}=
15
y
3
=
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Simplify.
\newline
Remove all perfect squares from inside the square root. Assume
\newline
b
b
b
is positive.
\newline
48
b
7
\sqrt{48b^{7}}
48
b
7
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
112
a
6
\sqrt{112a^{6}}
112
a
6
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Simplify.
\newline
Multiply and remove all perfect squares from inside the square roots. Assume
b
b
b
is positive.
\newline
24
b
3
⋅
40
b
2
⋅
b
2
=
\sqrt{24b^{3}}\cdot\sqrt{40b^{2}}\cdot\sqrt{b^{2}}=
24
b
3
⋅
40
b
2
⋅
b
2
=
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Simplify.
\newline
Multiply and remove all perfect squares from inside the square roots. Assume
\newline
b
b
b
is positive.
\newline
2
8
b
3
⋅
9
18
b
=
2\sqrt{8b^{3}} \cdot 9\sqrt{18b} =
2
8
b
3
⋅
9
18
b
=
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Simplify. Assume
x
x
x
is greater than or equal to zero.
\newline
20
x
3
\sqrt{20x^3}
20
x
3
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