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Math Problems
Algebra 1
Multiply radical expressions
7
−
13
−
7
+
13
\sqrt{7-\sqrt{13}}-\sqrt{7+\sqrt{13}}
7
−
13
−
7
+
13
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7
−
13
×
7
+
13
\sqrt{7-\sqrt{13}}\times\sqrt{7+\sqrt{13}}
7
−
13
×
7
+
13
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2
5
6
+
2
2
3
\frac{2\sqrt{5}}{\sqrt{6}} + \frac{2\sqrt{2}}{\sqrt{3}}
6
2
5
+
3
2
2
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Select all the numbers that are irrational.
\newline
Multi-select Choices:
\newline
(A)
−
144
-\sqrt{144}
−
144
\newline
(B)
−
150
-\sqrt{150}
−
150
\newline
(C)
−
75
-\sqrt{75}
−
75
\newline
(D)
−
50
-\sqrt{50}
−
50
\newline
(E)
−
100
-\sqrt{100}
−
100
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ice
5
5
5
Multiply, using the approach that seems easiest to you.
\newline
(
5
x
+
10
)
2
(\sqrt{5 x}+\sqrt{10})^{2}
(
5
x
+
10
)
2
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(
3
x
9
y
3
)
2
\left(3 x^{9} y^{3}\right)^{2}
(
3
x
9
y
3
)
2
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23
23
23
)
3
2
\frac{\sqrt{3}}{\sqrt{2}}
2
3
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Simplify.
\newline
2
⋅
6
\sqrt{2} \cdot \sqrt{6}
2
⋅
6
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Which is equivalent to
5
3
\frac{\sqrt{5}}{\sqrt{3}}
3
5
?
\newline
A.
5
3
\frac{\sqrt{5}}{3}
3
5
\newline
B.
15
3
\frac{\sqrt{15}}{3}
3
15
\newline
C.
5
3
\frac{5}{3}
3
5
\newline
D.
5
3
\frac{5}{\sqrt{3}}
3
5
\newline
E.
3
15
\frac{3}{\sqrt{15}}
15
3
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9
9
9
.
(
4
+
3
)
(
4
−
3
)
(4+\sqrt{3})(4-\sqrt{3})
(
4
+
3
)
(
4
−
3
)
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Simplify:
6
(
4
x
−
5
)
6(4 x-5)
6
(
4
x
−
5
)
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4
x
[
x
+
2
(
x
+
5
)
]
4 x[x+2(x+5)]
4
x
[
x
+
2
(
x
+
5
)]
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(
x
+
2
)
4
(x+2)^{4}
(
x
+
2
)
4
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Compute the multiplication of the square roots and simplify.
\newline
14
×
7
\sqrt{14} \times \sqrt{7}
14
×
7
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(c)
\newline
1
+
5
1
−
5
\frac{1+\sqrt{5}}{1-\sqrt{5}}
1
−
5
1
+
5
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Multiply. Write your answer in simplest form.
\newline
15
×
5
\sqrt{15} \times \sqrt{5}
15
×
5
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Simplify. Write your answer in simplest form.
\newline
(
15
)
2
(\sqrt{15})^{2}
(
15
)
2
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Multiply. Write your answer in simplest form.
\newline
6
×
2
\sqrt{6} \times \sqrt{2}
6
×
2
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Multiply. Write your answer in simplest form.
\newline
2
×
5
\sqrt{2}\times\sqrt{5}
2
×
5
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Multiply. Write your answer in simplest form.
\newline
3
×
2
\sqrt{3} \times \sqrt{2}
3
×
2
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Calculate the product and reduce to the lowest terms.
\newline
8
×
2
\sqrt{8}\times\sqrt{2}
8
×
2
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Find the result of the following operation in its simplest form.
\newline
10
⋅
3
\sqrt{10}\cdot\sqrt{3}
10
⋅
3
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Perform the multiplication and express the result in the simplest form.
\newline
12
×
4
\sqrt{12}\times\sqrt{4}
12
×
4
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Determine the simplest product of the two square roots.
\newline
18
×
6
\sqrt{18} \times \sqrt{6}
18
×
6
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d)
pizza
⋅
pizza
\sqrt{\text{pizza}} \cdot \sqrt{\text{pizza}}
pizza
⋅
pizza
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Home w
\newline
(
3
+
7
)
(
4
−
13
)
(3+\sqrt{7})(4-\sqrt{13})
(
3
+
7
)
(
4
−
13
)
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(
x
)
3
=
x
(
x
)
(\sqrt{x})^{3}=x(\sqrt{x})
(
x
)
3
=
x
(
x
)
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Home wouk
\newline
(
3
+
7
)
(
4
−
13
)
(3+\sqrt{7})(4-\sqrt{13})
(
3
+
7
)
(
4
−
13
)
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Solve the equation.
\newline
5
x
+
1
−
1
=
3
x
\sqrt{5 x+1}-1=\sqrt{3 x}
5
x
+
1
−
1
=
3
x
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Simplify.
\newline
5
+
3
5
−
3
+
5
−
3
5
+
3
\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}+\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}
5
−
3
5
+
3
+
5
+
3
5
−
3
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Simplify.
\newline
2
3
+
2
\frac{2}{3+\sqrt{2}}
3
+
2
2
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Simplify.
\newline
1
3
+
1
2
\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{2}}
3
1
+
2
1
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Evaluate the expression.
\newline
8
⋅
9
+
3
(
6
−
7
)
8 \cdot 9 + 3(6 - 7)
8
⋅
9
+
3
(
6
−
7
)
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Solve.
\newline
u
−
3
u
−
9
×
u
+
3
u
+
3
\frac{\sqrt{u}-3}{u-9} \times \frac{\sqrt{u}+3}{\sqrt{u}+3}
u
−
9
u
−
3
×
u
+
3
u
+
3
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Solve for
b
b
b
.
\newline
b
+
1
=
b
+
6
−
1
\sqrt{b+1}=\sqrt{b+6}-1
b
+
1
=
b
+
6
−
1
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Simplify.
\newline
(
5
−
2
)
2
(\sqrt{5}-\sqrt{2})^{2}
(
5
−
2
)
2
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Simplify.
\newline
4
3
+
5
\frac{4}{3+\sqrt{5}}
3
+
5
4
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Simplify.
\newline
(
2
x
+
2
)
4
−
(
x
+
1
)
4
(2 x+2)^{4}-(x+1)^{4}
(
2
x
+
2
)
4
−
(
x
+
1
)
4
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v
3
⋅
v
\sqrt[3]{v} \cdot \sqrt{v}
3
v
⋅
v
=
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Integrate.
\newline
∫
x
⋅
arctan
x
d
x
\int \sqrt{x} \cdot \operatorname{arctan} \sqrt{x} d x
∫
x
⋅
arctan
x
d
x
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Simplify.
\newline
(
2
−
3
)
7
+
4
3
\sqrt{(2-\sqrt{3}) \sqrt{7+4 \sqrt{3}}}
(
2
−
3
)
7
+
4
3
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5
2
x
+
5
−
1
2
x
+
5
+
2
\frac{5 \sqrt{2 x+5}-1}{\sqrt{2 x+5}+2}
2
x
+
5
+
2
5
2
x
+
5
−
1
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Click and drag like terms onto each other to simplify fully.
\newline
−
5
−
2
y
+
2
+
5
+
2
x
-5-2 y+2+5+2 x
−
5
−
2
y
+
2
+
5
+
2
x
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∫
(
2
x
+
6
)
5
d
x
\int(2x+6)^5\,dx
∫
(
2
x
+
6
)
5
d
x
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Try these:
\newline
a)
(
i
)
2
(\sqrt{i})^{2}
(
i
)
2
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−
1
⋅
−
1
\sqrt{-1} \cdot \sqrt{-1}
−
1
⋅
−
1
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(
1
+
2
)
7
+
(
1
−
2
)
7
(1+\sqrt{2})^{7}+(1-\sqrt{2})^{7}
(
1
+
2
)
7
+
(
1
−
2
)
7
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Multiply. Write your answer in simplest form.
\newline
15
×
2
\sqrt{15} \times \sqrt{2}
15
×
2
\newline
_____________
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