To determine which statements are true or false, let's compare rational approximations of the given square roots.
1. Statement: [tex]\(\sqrt{71} < \sqrt{61}\)[/tex]
- The square root of 71 is approximately 8.426.
- The square root of 61 is approximately 7.810.
- Since 8.426 is not less than 7.810, this statement is False.
2. Statement: [tex]\(\sqrt{81} > 9\)[/tex]
- The square root of 81 is exactly 9.
- Since 9 is not greater than 9, this statement is False.
3. Statement: [tex]\(\sqrt{71} > \sqrt{61}\)[/tex]
- The square root of 71 is approximately 8.426.
- The square root of 61 is approximately 7.810.
- Since 8.426 is indeed greater than 7.810, this statement is True.
4. Statement: [tex]\(\sqrt{81} < 9\)[/tex]
- The square root of 81 is exactly 9.
- Since 9 is not less than 9, this statement is False.
Based on the evaluations, the true statement is:
- [tex]\(\sqrt{71} > \sqrt{61}\)[/tex]
Therefore, the correct answer is:
[tex]\(\sqrt{71} > \sqrt{61}\)[/tex]
