Question
Question
Using rational approximations, what statement is true?(1 point)
Responses
16−−√>4
start root 16 end root greater than 4
16 −−−√<4
start root 16 end root less than 4
12 −−−√ >π
start root 12 end root greater than pi
12 −−−√<π
Using rational approximations, what statement is true?(1 point)
Responses
16−−√>4
start root 16 end root greater than 4
16 −−−√<4
start root 16 end root less than 4
12 −−−√ >π
start root 12 end root greater than pi
12 −−−√<π
Answers
GPT-4o mini
Let's evaluate the statements one by one.
1. **\(\sqrt{16} > 4\)**: This is false because \(\sqrt{16} = 4\).
2. **\(\sqrt{16} < 4\)**: This is also false for the same reason; \(\sqrt{16} = 4\).
3. **\(\sqrt{12} > \pi\)**: To evaluate this, we can approximate. \(\sqrt{12} \approx 3.464\) and \(\pi \approx 3.14\), so \(\sqrt{12} > \pi\) is true.
4. **\(\sqrt{12} < \pi\)**: Since \(\sqrt{12} \approx 3.464\) is greater than \(\pi \approx 3.14\), this statement is false.
Thus, the true statement based on rational approximations is:
\(\sqrt{12} > \pi\)
1. **\(\sqrt{16} > 4\)**: This is false because \(\sqrt{16} = 4\).
2. **\(\sqrt{16} < 4\)**: This is also false for the same reason; \(\sqrt{16} = 4\).
3. **\(\sqrt{12} > \pi\)**: To evaluate this, we can approximate. \(\sqrt{12} \approx 3.464\) and \(\pi \approx 3.14\), so \(\sqrt{12} > \pi\) is true.
4. **\(\sqrt{12} < \pi\)**: Since \(\sqrt{12} \approx 3.464\) is greater than \(\pi \approx 3.14\), this statement is false.
Thus, the true statement based on rational approximations is:
\(\sqrt{12} > \pi\)