Question
... Using rational approximations, what statement is true?(1 point) Responses 81−−√<9 start root 81 end root less than 9 81−−√>9 start root 81 end root greater than 9 71 −−−√<61−−√ start root 71 end root less than start root 61 end root 71−−√>61−−√ start root 71 end root greater than start root 61 end root
Answers
GPT-4o mini
To analyze the given inequalities, let's evaluate them one by one.
1. **First inequality: \(\sqrt{81} < 9\)**
We find that \(\sqrt{81} = 9\). Thus, the statement \(\sqrt{81} < 9\) is false.
2. **Second inequality: \(\sqrt{81} > 9\)**
As previously calculated, \(\sqrt{81} = 9\). Thus, the statement \(\sqrt{81} > 9\) is also false.
3. **Third inequality: \(\sqrt{71} < \sqrt{61}\)**
Taking the approximations:
- \(\sqrt{71} \approx 8.426\)
- \(\sqrt{61} \approx 7.810\)
Therefore, \(\sqrt{71} > \sqrt{61}\) is true. The statement \(\sqrt{71} < \sqrt{61}\) is false.
4. **Fourth inequality: \(\sqrt{71} > \sqrt{61}\)**
As derived above, this is true since \(\sqrt{71} \approx 8.426\) and \(\sqrt{61} \approx 7.810\).
**Conclusion**:
The only true statement among the given options is:
\(\sqrt{71} > \sqrt{61}\).
1. **First inequality: \(\sqrt{81} < 9\)**
We find that \(\sqrt{81} = 9\). Thus, the statement \(\sqrt{81} < 9\) is false.
2. **Second inequality: \(\sqrt{81} > 9\)**
As previously calculated, \(\sqrt{81} = 9\). Thus, the statement \(\sqrt{81} > 9\) is also false.
3. **Third inequality: \(\sqrt{71} < \sqrt{61}\)**
Taking the approximations:
- \(\sqrt{71} \approx 8.426\)
- \(\sqrt{61} \approx 7.810\)
Therefore, \(\sqrt{71} > \sqrt{61}\) is true. The statement \(\sqrt{71} < \sqrt{61}\) is false.
4. **Fourth inequality: \(\sqrt{71} > \sqrt{61}\)**
As derived above, this is true since \(\sqrt{71} \approx 8.426\) and \(\sqrt{61} \approx 7.810\).
**Conclusion**:
The only true statement among the given options is:
\(\sqrt{71} > \sqrt{61}\).