Question

Using rational approximations, what statement is true?(1 point)
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 less than pi 12 −−−√ >π

Answer 1

To evaluate the statements regarding the square roots and their comparisons with known values or constants, let's analyze each statement one by one.

1. **\( \sqrt{16} > 4 \)**:
- We calculate \( \sqrt{16} = 4 \).
- Therefore, this statement is **false**.

2. **\( \sqrt{16} < 4 \)**:
- As previously calculated, \( \sqrt{16} = 4 \).
- Therefore, this statement is also **false**.

3. **\( \sqrt{12} < \pi \)**:
- We know \( \pi \approx 3.14 \).
- \( \sqrt{12} \approx 3.464 \) (since \( \sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3} \), and \( \sqrt{3} \approx 1.732\)).
- Thus \( \sqrt{12} > \pi \), making this statement **false**.

4. **\( \sqrt{12} > \pi \)**:
- As we calculated, \( \sqrt{12} \approx 3.464 \) and \( \pi \approx 3.14 \).
- Therefore, \( \sqrt{12} > \pi \) is **true**.

From the analysis, the statement that is true is:

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