Question

Using rational approximations, what statement is true?(1 point) Responses 12 −−−√ >π start root 12 end root greater than pi 16 −−−√<4 start root 16 end root less than 4 16−−√>4 start root 16 end root greater than 4 12 −−−√<π

Answer 1

To determine which statement is true using rational approximations, let's evaluate each expression:

1. \( \sqrt{12} \) vs. \( \pi \):
- \( \sqrt{12} \approx 3.464 \)
- \( \pi \approx 3.14159 \)
- Therefore, \( \sqrt{12} > \pi \) is true.

2. \( \sqrt{16} \) vs. 4:
- \( \sqrt{16} = 4 \)
- Therefore, \( \sqrt{16} < 4 \) is false.
- \( \sqrt{16} > 4 \) is false.
- \( \sqrt{16} = 4 \) is true.

3. \( \sqrt{12} < \pi \):
- As previously calculated, \( \sqrt{12} > \pi \), so this is false.

From these evaluations, the correct true statement is:
**\( \sqrt{12} > \pi \)**.