Let's analyze each statement one by one, using the given results:
1. Statement: [tex]\(\sqrt{81} > 9\)[/tex]
- The square root of 81 is calculated to be 9.0.
- Since 9.0 is equal to 9, the statement [tex]\(\sqrt{81} > 9\)[/tex] is false.
2. 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.
- Comparing these two approximations, we see that 8.426 is not less than 7.810, so the statement [tex]\(\sqrt{71} < \(\sqrt{61}\)[/tex] is false.
3. Statement: [tex]\(\sqrt{71} > \(\sqrt{61}\)[/tex]
- Again, the square root of 71 is approximately 8.426.
- The square root of 61 is approximately 7.810.
- Since 8.426 is greater than 7.810, the statement [tex]\(\sqrt{71} > \(\sqrt{61}\)[/tex] is true.
4. Statement: [tex]\(\sqrt{81} < 9\)[/tex]
- The square root of 81 is 9.0.
- Since 9.0 is equal to 9, the statement [tex]\(\sqrt{81} < 9\)[/tex] is false.
So, the true statement among the given options is:
[tex]\[ \sqrt{71} > \sqrt{61} \][/tex]
