Question

Using rational approximations, what statement is true?

12 −−−√<π
start root 12 end root less than pi

16−−√>4
start root 16 end root greater than 4

12 −−−√ >π
start root 12 end root greater than pi

16 −−−√<4

Answer 1

To evaluate the statements using rational approximations, we first need to calculate the numerical values or approximations for the square roots and the constant π (pi).

1. **Calculating the square roots:**
- \( \sqrt{12} \approx 3.464 \)
- \( \sqrt{16} = 4 \)

2. **Using the approximation for π:**
- \( \pi \approx 3.14159 \)

Now let's examine each statement:

1. **\( \sqrt{12} < \pi \)**:
- \( 3.464 < 3.14159 \) is false.

2. **\( \sqrt{16} > 4 \)**:
- \( 4 > 4 \) is false (it is equal, not greater).

3. **\( \sqrt{12} > \pi \)**:
- \( 3.464 > 3.14159 \) is true.

4. **\( \sqrt{16} < 4 \)**:
- \( 4 < 4 \) is false (it is equal, not less).

Based on these evaluations, the true statement is:

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