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Math Problems
Algebra 2
Simplify radical expressions using conjugates
Rationalise the denominators of
1
2
+
3
+
5
\frac{1}{\sqrt{2}} + \sqrt{3} + \sqrt{5}
2
1
+
3
+
5
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Simplify. Rationalize the denominator.
\newline
6
−
9
−
5
\frac{6}{-9 - \sqrt{5}}
−
9
−
5
6
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Simplify. Rationalize the denominator.
\newline
4
4
+
5
\frac{4}{4 + \sqrt{5}}
4
+
5
4
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Simplify. Rationalize the denominator.
\newline
5
5
+
3
\frac{5}{5 + \sqrt{3}}
5
+
3
5
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Simplify. Rationalize the denominator.
\newline
5
−
6
−
5
\frac{5}{-6 - \sqrt{5}}
−
6
−
5
5
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Simplify. Rationalize the denominator.
\newline
5
−
6
+
5
\frac{5}{-6 + \sqrt{5}}
−
6
+
5
5
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Simplify. Rationalize the denominator.
\newline
4
9
+
3
\frac{4}{9 + \sqrt{3}}
9
+
3
4
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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
9
5
+
5
\frac{9}{5 + \sqrt{5}}
5
+
5
9
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Simplify. Rationalize the denominator.
\newline
3
−
7
−
3
\frac{3}{-7 - \sqrt{3}}
−
7
−
3
3
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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
4
+
3
\frac{10}{4 + \sqrt{3}}
4
+
3
10
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Simplify. Rationalize the denominator.
\newline
10
5
−
5
\frac{10}{5 - \sqrt{5}}
5
−
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
−
5
+
2
\frac{4}{-5 + \sqrt{2}}
−
5
+
2
4
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Simplify. Rationalize the denominator.
\newline
3
−
6
+
5
\frac{3}{-6 + \sqrt{5}}
−
6
+
5
3
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Simplify. Rationalize the denominator.
\newline
9
3
+
2
\frac{9}{3 + \sqrt{2}}
3
+
2
9
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Simplify. Rationalize the denominator.
\newline
10
−
10
+
5
\frac{10}{-10 + \sqrt{5}}
−
10
+
5
10
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Simplify. Rationalize the denominator.
\newline
7
−
7
+
5
\frac{7}{-7 + \sqrt{5}}
−
7
+
5
7
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Simplify. Rationalize the denominator.
\newline
3
−
4
+
3
\frac{3}{-4 + \sqrt{3}}
−
4
+
3
3
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Simplify. Rationalize the denominator.
\newline
5
−
10
+
2
\frac{5}{-10 + \sqrt{2}}
−
10
+
2
5
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Simplify. Rationalize the denominator.
\newline
10
−
3
+
5
\frac{10}{-3 + \sqrt{5}}
−
3
+
5
10
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Simplify. Rationalize the denominator.
\newline
2
−
2
+
3
\frac{2}{-2 + \sqrt{3}}
−
2
+
3
2
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Simplify. Rationalize the denominator.
\newline
2
−
2
+
5
\frac{2}{-2 + \sqrt{5}}
−
2
+
5
2
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Simplify. Rationalize the denominator.
\newline
6
2
+
3
\frac{6}{2 + \sqrt{3}}
2
+
3
6
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Simplify. Rationalize the denominator.
\newline
3
−
9
−
2
\frac{3}{-9 - \sqrt{2}}
−
9
−
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
5
−
2
−
2
\frac{5}{-2 - \sqrt{2}}
−
2
−
2
5
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Simplify. Rationalize the denominator.
\newline
5
−
4
−
3
\frac{5}{-4 - \sqrt{3}}
−
4
−
3
5
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Simplify. Rationalize the denominator.
\newline
3
6
+
3
\frac{3}{6 + \sqrt{3}}
6
+
3
3
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Simplify. Rationalize the denominator.
\newline
10
−
8
+
3
\frac{10}{-8 + \sqrt{3}}
−
8
+
3
10
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Simplify. Rationalize the denominator.
\newline
9
−
8
−
2
\frac{9}{-8 - \sqrt{2}}
−
8
−
2
9
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Simplify. Rationalize the denominator.
\newline
8
8
+
3
\frac{8}{8 + \sqrt{3}}
8
+
3
8
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Simplify. Rationalize the denominator.
\newline
4
−
8
−
5
\frac{4}{-8 - \sqrt{5}}
−
8
−
5
4
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Simplify. Rationalize the denominator.
\newline
2
−
8
−
3
\frac{2}{-8 - \sqrt{3}}
−
8
−
3
2
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Simplify. Rationalize the denominator.
\newline
6
−
5
−
5
\frac{6}{-5 - \sqrt{5}}
−
5
−
5
6
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Simplify. Rationalize the denominator.
\newline
9
−
5
+
5
\frac{9}{-5 + \sqrt{5}}
−
5
+
5
9
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Simplify. Rationalize the denominator.
\newline
5
−
9
+
5
\frac{5}{-9 + \sqrt{5}}
−
9
+
5
5
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Simplify. Rationalize the denominator.
\newline
6
−
6
+
5
\frac{6}{-6 + \sqrt{5}}
−
6
+
5
6
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Simplify. Rationalize the denominator.
\newline
8
−
5
+
3
\frac{8}{-5 + \sqrt{3}}
−
5
+
3
8
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Simplify. Rationalize the denominator.
\newline
4
−
9
−
2
\frac{4}{-9 - \sqrt{2}}
−
9
−
2
4
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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
3
+
2
\frac{10}{3 + \sqrt{2}}
3
+
2
10
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Simplify. Rationalize the denominator.
\newline
10
−
2
+
3
\frac{10}{-2 + \sqrt{3}}
−
2
+
3
10
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Simplify. Rationalize the denominator.
\newline
4
−
5
−
5
\frac{4}{-5 - \sqrt{5}}
−
5
−
5
4
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Simplify. Rationalize the denominator.
\newline
5
−
6
−
3
\frac{5}{-6 - \sqrt{3}}
−
6
−
3
5
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Simplify. Rationalize the denominator.
\newline
10
−
5
+
2
\frac{10}{-5 + \sqrt{2}}
−
5
+
2
10
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Simplify. Rationalize the denominator.
\newline
8
2
−
2
\frac{8}{2 - \sqrt{2}}
2
−
2
8
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Simplify. Rationalize the denominator.
\newline
9
−
5
+
2
\frac{9}{-5 + \sqrt{2}}
−
5
+
2
9
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Simplify. Rationalize the denominator.
\newline
2
−
9
+
2
\frac{2}{-9 + \sqrt{2}}
−
9
+
2
2
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1
2
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