To evaluate the statements using rational approximations, we first find the square roots of the relevant numbers:
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For the first statement:
- \( \sqrt{81} = 9 \)
- Therefore, \( \sqrt{81} = 9 \) and the statement \( \sqrt{81} < 9 \) is false, while \( \sqrt{81} > 9 \) is also false.
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For the second statement:
- \( \sqrt{71} \) is approximately \( 8.426 \)
- \( \sqrt{61} \) is approximately \( 7.810 \)
- Therefore, \( \sqrt{71} > \sqrt{61} \) is true, while \( \sqrt{71} < \sqrt{61} \) is false.
From this analysis, the true statement is:
\( \sqrt{71} > \sqrt{61} \).