Question

Using rational approximations, what statement is true?

responses

√16 > 4

√12 < π

√16 < 4

√12 > π

Answer 1

what’s the right answwr

Answer 2

To evaluate the statements, we can calculate the values of the square roots and compare them with π.

1. **√16 > 4**:
- √16 = 4
- This statement is false; 4 is not greater than 4.

2. **√12 < π**:
- √12 ≈ 3.464 (since √12 = √(4*3) = 2√3 and √3 ≈ 1.732)
- π ≈ 3.14
- This statement is true; 3.464 is less than 3.14.

3. **√16 < 4**:
- As calculated, √16 = 4.
- This statement is false; 4 is not less than 4.

4. **√12 > π**:
- As calculated, √12 ≈ 3.464 and π ≈ 3.14.
- This statement is false; 3.464 is not greater than 3.14.

Based on these evaluations, the true statement is:

**√12 < π**.

Answer 3

Apologies for the confusion in my previous explanation. Let's re-evaluate the statements correctly:

1. **√16 > 4**:
- √16 = 4.
- This statement is **false**.

2. **√12 < π**:
- √12 ≈ 3.464 (since √12 = 2√3 and √3 ≈ 1.732).
- π ≈ 3.14.
- This statement is **true** because 3.464 (√12) is greater than 3.14 (π), incorrect in my previous message.

3. **√16 < 4**:
- Again, √16 = 4.
- This statement is **false**.

4. **√12 > π**:
- As previously calculated, √12 ≈ 3.464, which is less than π ≈ 3.14.
- This statement is **false**.

So, the correct analysis shows that:

- **The true statement is:** **√12 > π** is **false**; rather, **√12 < π** is the true statement.

Therefore, the accurate conclusion based on rational approximations is:

**√12 < π** is **true**.