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Tests on rationalizing denominator
Rationalizing denominator with two or more terms
Rationalizing denominator with two or more terms
ans:
syntax error
C
DEL
ANS
±
(
)
÷
×
7
8
9
–
4
5
6
+
1
2
3
=
0
.
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Question 1:
1 pts
The conjugate of
2
+
2
2+\sqrt{2}
2
+
2
is
2
−
2
2-\sqrt{2}
2
−
2
Question 2:
1 pts
The conjugate of
−
a
−
1
-\sqrt{a}-1
−
a
−
1
is
a
+
1
\sqrt{a}+1
a
+
1
Question 3:
1 pts
To rationalize denominator in
1
2
+
1
\frac{1}{\sqrt{2}+1}
2
+
1
1
we multiply both numerator and denominator with.
1
+
2
1+\sqrt{2}
1
+
2
1
−
2
1-\sqrt{2}
1
−
2
2
−
1
\sqrt{2}-1
2
−
1
Question 4:
1 pts
To rationalize denominator in
1
3
−
2
\frac{1}{\sqrt{3}-\sqrt{2}}
3
−
2
1
we multiply both numerator and denominator with.
3
+
2
\sqrt{3}+\sqrt{2}
3
+
2
3
−
2
\sqrt{3}-\sqrt{2}
3
−
2
2
−
3
\sqrt{2}-\sqrt{3}
2
−
3
Question 5:
1 pts
Is the following equation true or false:
1
3
−
2
=
3
+
2
\frac{1}{\sqrt{3}-\sqrt{2}} = \sqrt{3}+\sqrt{2}
3
−
2
1
=
3
+
2
Question 6:
2 pts
Rationalize denominator
1
2
−
3
\frac{1}{2-\sqrt{3}}
2
−
3
1
4
+
3
4+\sqrt{3}
4
+
3
4
−
3
4-\sqrt{3}
4
−
3
2
+
3
2+\sqrt{3}
2
+
3
Question 7:
2 pts
Rationalize denominator:
3
−
2
3
+
2
\frac{\sqrt{3} - \sqrt{2} } {\sqrt{3} + \sqrt{2}}
3
+
2
3
−
2
5
+
6
5 + \sqrt{6}
5
+
6
5
−
6
5 - \sqrt{6}
5
−
6
5
+
2
6
5 + 2\sqrt{6}
5
+
2
6
5
−
2
6
5 - 2\sqrt{6}
5
−
2
6
Question 8:
2 pts
Rationalize denominator:
20
20
−
10
\frac{20} {\sqrt{20} - \sqrt{10}}
20
−
10
20
20
(
20
+
10
)
10
\frac{20(\sqrt{20} +\sqrt{10})}{10}
10
20
(
20
+
10
)
2
(
20
+
10
)
2(\sqrt{20} +\sqrt{10})
2
(
20
+
10
)
2
(
20
−
10
)
2(\sqrt{20} - \sqrt{10})
2
(
20
−
10
)
Question 9:
3 pts
Is the following equation true or false:
8
+
2
2
−
2
=
9
+
5
2
\frac{8+\sqrt{2}}{2-\sqrt{2}}=9+5\sqrt{2}
2
−
2
8
+
2
=
9
+
5
2
Question 10:
3 pts
Is the following equation true or false:
3
+
4
2
−
3
=
3
+
2
2
+
2
3
+
6
\frac{\sqrt{3}+\sqrt{4}}{\sqrt{2}-\sqrt{3}}=3+2\sqrt{2}+2\sqrt{3}+\sqrt{6}
2
−
3
3
+
4
=
3
+
2
2
+
2
3
+
6
Question 11:
3 pts
Rationalize denominator:
a
a
+
1
\frac{\sqrt{a}} {\sqrt{a} + 1}
a
+
1
a
a
−
a
a
−
1
\frac{a-\sqrt{a}}{a-1}
a
−
1
a
−
a
a
−
a
a
+
1
\frac{a-\sqrt{a}}{a+1}
a
+
1
a
−
a
a
a
−
1
\frac{a}{a-1}
a
−
1
a
a
a
+
1
\frac{\sqrt{a}}{a+1}
a
+
1
a
Question 12:
3 pts
Rationalize denominator:
x
2
−
9
3
−
x
\frac{x^2-9} {\sqrt{3} - \sqrt{x}}
3
−
x
x
2
−
9
(
x
+
3
)
(
3
+
x
)
(x+3)(\sqrt{3}+\sqrt{x})
(
x
+
3
)
(
3
+
x
)
−
(
x
+
3
)
(
3
+
x
)
-(x+3)(\sqrt{3} + \sqrt{x})
−
(
x
+
3
)
(
3
+
x
)
(
x
+
3
)
(
x
−
3
)
(x+3)(\sqrt{x}-\sqrt{3})
(
x
+
3
)
(
x
−
3
)
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Exponents and Logarithms
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Algebra 2
Geometry
Solid Figures
Basic operations
Simplifying Radicals
Adding and subtracting square roots
Multiplying square roots
Rationalizing denominator
One radical term
Two or more terms
Radical equations & inequalities
Solving equations
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