To determine which statement is true, we can evaluate or approximate the square roots in each option:
a) \( \sqrt{81} > 9 \)
- We know \( \sqrt{81} = 9 \), so this statement is false.
b) \( \sqrt{71} > \sqrt{61} \)
- Since 71 is greater than 61, their square roots can be compared. Indeed, \( \sqrt{71} \) is greater than \( \sqrt{61} \). So this statement is true.
c) \( \sqrt{71} < \sqrt{61} \)
- Since \( \sqrt{71} \) is greater than \( \sqrt{61} \), this statement is false.
d) \( \sqrt{81} < 9 \)
- As mentioned before, \( \sqrt{81} = 9 \), so this statement is false.
The only true statement is b) \( \sqrt{71} > \sqrt{61} \).