Using rational approximations, what statement is true?(1 point)

Question

16−−√>4
16 −−−√<4
12 −−−√<π
12 −−−√ >π

Answer 1

To analyze the statements using rational approximations, let's evaluate each one:

1. \( \sqrt{16} > 4 \):
   \( \sqrt{16} = 4 \)
   So, \( \sqrt{16} > 4 \) is false.

2. \( \sqrt{16} < 4 \):
   \( \sqrt{16} = 4 \)
   So, \( \sqrt{16} < 4 \) is false.

3. \( \sqrt{12} < \pi \):
   We know \( \sqrt{12} \approx 3.464 \) and \( \pi \approx 3.14159 \).
   So, \( \sqrt{12} < \pi \) is false.

4. \( \sqrt{12} > \pi \):
   Given \( \sqrt{12} \approx 3.464 \) and \( \pi \approx 3.14159 \),
   We find \( \sqrt{12} > \pi \) is true.

Therefore, the correct statement is: \( \sqrt{12} > \pi \).