To determine the correctness of the statements using rational approximations, let's examine each one:
A. \( \sqrt{71} < \sqrt{61} \)
- This is false because both numbers are positive, and 71 is greater than 61, so \( \sqrt{71} > \sqrt{61} \).
B. \( \sqrt{71} > \sqrt{61} \)
- This is true for the same reason as above. Since 71 is greater than 61, \( \sqrt{71} \) is indeed greater than \( \sqrt{61} \).
C. \( \sqrt{81} < 9 \)
- This is false because \( \sqrt{81} = 9 \).
D. \( \sqrt{81} > 9 \)
- This is also false because \( \sqrt{81} = 9 \).
From the evaluations above, the true statement is B. \( \sqrt{71} > \sqrt{61} \).
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