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Math Problems
Algebra 1
Simplify radical expressions using conjugates
Rationalise the denominators, simplifying your answer where possible:
\newline
1
7
\frac{1}{\sqrt{7}}
7
1
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Ratinalise denominator :-
\newline
7
+
3
5
7
−
3
5
\frac{7+3 \sqrt{5}}{7-3 \sqrt{5}}
7
−
3
5
7
+
3
5
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First, write the subtraction so the fractions have denominator
10
10
10
. Then subtract.
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Find the length of side
x
x
x
in simplest radical form with a rational denominator.
\newline
Answer Attempt
1
1
1
out of
2
2
2
\newline
x
=
x=
x
=
\newline
□
\square
□
\newline
Submit Answer
\newline
\sqrt{ }
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Simplify
6
−
4
3
6
+
4
3
\frac{6-4 \sqrt{3}}{6+4 \sqrt{3}}
6
+
4
3
6
−
4
3
by rationalizing the denominator.
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Simplify. Rationalize the denominator.
\newline
2
−
6
−
2
\frac{2}{-6 - \sqrt{2}}
−
6
−
2
2
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Simplify. Rationalize the denominator.
\newline
3
−
7
−
5
\frac{3}{-7 - \sqrt{5}}
−
7
−
5
3
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Simplify. Rationalize the denominator.
\newline
6
−
6
−
3
\frac{6}{-6 - \sqrt{3}}
−
6
−
3
6
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Simplify. Rationalize the denominator.
\newline
10
−
10
−
3
\frac{10}{-10 - \sqrt{3}}
−
10
−
3
10
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Simplify. Rationalize the denominator.
\newline
10
−
7
−
5
\frac{10}{-7 - \sqrt{5}}
−
7
−
5
10
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Simplify. Rationalize the denominator.
\newline
10
−
9
−
2
\frac{10}{-9 - \sqrt{2}}
−
9
−
2
10
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Simplify. Rationalize the denominator.
\newline
4
−
7
−
5
\frac{4}{-7 - \sqrt{5}}
−
7
−
5
4
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Simplify. Rationalize the denominator.
\newline
3
−
2
−
5
\frac{3}{-2 - \sqrt{5}}
−
2
−
5
3
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Simplify. Rationalize the denominator.
\newline
4
−
2
−
3
\frac{4}{-2 - \sqrt{3}}
−
2
−
3
4
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Simplify. Rationalize the denominator.
\newline
9
9
−
2
\frac{9}{9 - \sqrt{2}}
9
−
2
9
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Simplify. Rationalize the denominator.
\newline
8
−
2
−
3
\frac{8}{-2 - \sqrt{3}}
−
2
−
3
8
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4
4
4
. Write each expression in simplest form by rationalizing the denominator (
2
2
2
marks each)
\newline
a)
2
3
+
4
3
\frac{2 \sqrt{3}+4}{\sqrt{3}}
3
2
3
+
4
\newline
b)
3
5
+
2
2
\frac{\sqrt{3}}{\sqrt{5}+2 \sqrt{2}}
5
+
2
2
3
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Simplify. Rationalize the denominator.
\newline
3
−
6
−
2
\frac{3}{-6 - \sqrt{2}}
−
6
−
2
3
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Simplify. Rationalize the denominator.
\newline
9
−
9
−
2
\frac{9}{-9 - \sqrt{2}}
−
9
−
2
9
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Simplify. Rationalize the denominator.
\newline
7
−
9
−
5
\frac{7}{-9 - \sqrt{5}}
−
9
−
5
7
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Simplify. Rationalize the denominator.
\newline
8
−
5
−
2
\frac{8}{-5 - \sqrt{2}}
−
5
−
2
8
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Simplify. Rationalize the denominator.
\newline
9
−
9
−
5
\frac{9}{-9 - \sqrt{5}}
−
9
−
5
9
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Simplify. Rationalize the denominator.
\newline
8
4
−
5
\frac{8}{4 - \sqrt{5}}
4
−
5
8
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Simplify. Rationalize the denominator.
\newline
7
−
4
−
5
\frac{7}{-4 - \sqrt{5}}
−
4
−
5
7
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Simplify. Rationalize the denominator.
\newline
10
−
9
−
3
\frac{10}{-9 - \sqrt{3}}
−
9
−
3
10
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Simplify by rationalizing the denominator:
4
10
−
6
\frac{4}{\sqrt{10}-\sqrt{6}}
10
−
6
4
\newline
(
1
1
1
point)
\newline
10
+
6
\sqrt{10}+\sqrt{6}
10
+
6
\newline
4
4
4
\newline
4
10
+
4
6
4 \sqrt{10}+4 \sqrt{6}
4
10
+
4
6
\newline
4
10
−
4
6
16
−
2
15
\frac{4 \sqrt{10}-4 \sqrt{6}}{16-2 \sqrt{15}}
16
−
2
15
4
10
−
4
6
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Simplify. Rationalize the denominator.
\newline
−
2
8
+
5
\frac{-2}{8+\sqrt{5}}
8
+
5
−
2
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f
(
n
)
=
45
⋅
(
4
5
)
n
−
1
f(n)=45\cdot\left(\dfrac{4}{5}\right)^{\large{\,n-1}}
f
(
n
)
=
45
⋅
(
5
4
)
n
−
1
Complete the recursive formula of
f
(
n
)
f(n)
f
(
n
)
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Simplify. Rationalize the denominator.
\newline
`(-7)/(2 + \sqrt{5}\)`
\newline
______
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