Question

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

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:
**\( \sqrt{12} > \pi \)**.