To evaluate the given inequalities, let's approximate the square roots of the numbers involved.
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Estimate \(\sqrt{61}\):
- Since \(61\) is between \(49\) (\(\sqrt{49} = 7\)) and \(64\) (\(\sqrt{64} = 8\)), we know \(7 < \sqrt{61} < 8\).
- A closer approximation is \(\sqrt{61} \approx 7.81\).
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Calculate \(\sqrt{81}\):
- \(\sqrt{81} = 9\).
Now we can evaluate each statement:
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\(71 > \sqrt{61}\):
- Since \(71\) is greater than \(\sqrt{61} \approx 7.81\), this statement is true.
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\(81 < \sqrt{9}\):
- This does not hold since \(\sqrt{81} = 9\).
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\(81 > \sqrt{9}\):
- \(\sqrt{9} = 3\), and \(81 > 3\) is true.
-
\(71 < \sqrt{61}\):
- Since we estimated \(\sqrt{61} \approx 7.81\), this statement is false.
Based on these evaluations, the true statements are:
- 71 > \(\sqrt{61}\)
- 81 > \(\sqrt{9}\)
However, the only statement that stands out as universally true given the context of the question is the first one:
\(71 > \sqrt{61}\) is a true statement.