Let's analyze each number set to determine if it contains rational or irrational numbers.
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Set: \( (\sqrt{2}, \sqrt{5}, \pi) \)
- \( \sqrt{2} \) and \( \sqrt{5} \) are irrational numbers.
- \( \pi \) is also an irrational number.
- Description: Irrational numbers only
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Set: \( (-7.4, 0, 3.232323..., \sqrt{25}) \)
- \(-7.4\) is a rational number.
- \(0\) is a rational number.
- \(3.232323...\) (which can be represented as \(3.\overline{23}\)) is a rational number.
- \( \sqrt{25} = 5 \) is a rational number.
- Description: Rational numbers only
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Set: \( (-\frac{5}{6}, \frac{7}{8}, \frac{\pi}{2}) \)
- \(-\frac{5}{6}\) and \(\frac{7}{8}\) are rational numbers.
- \(\frac{\pi}{2}\) is an irrational number (as \(\pi\) is irrational).
- Description: Both rational and irrational
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Set: \( (\sqrt{8}, \sqrt{9}, \sqrt{10}) \)
- \( \sqrt{8} = 2\sqrt{2} \) is irrational.
- \( \sqrt{9} = 3 \) is rational.
- \( \sqrt{10} \) is irrational.
- Description: Both rational and irrational
Based on this analysis, here is the summary for each set:
- \( (\sqrt{2}, \sqrt{5}, \pi) \) - Irrational numbers only
- \( (-7.4, 0, 3.232323..., \sqrt{25}) \) - Rational numbers only
- \( (-\frac{5}{6}, \frac{7}{8}, \frac{\pi}{2}) \) - Both rational and irrational
- \( (\sqrt{8}, \sqrt{9}, \sqrt{10}) \) - Both rational and irrational