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