Question

Using rational approximations, what statement is true?

responses

√16 > 4

√12 < 4

√16 < 4

√12 > π

Answer 1

To evaluate the statements using rational approximations:

1. **√16 > 4**: This is false because \( \sqrt{16} = 4 \).

2. **√12 < 4**: Let's evaluate this. \( \sqrt{12} \) is approximately \( 3.464 \), which is less than \( 4 \). This statement is true.

3. **√16 < 4**: This is false since \( \sqrt{16} = 4 \).

4. **√12 > π**: Since \( \pi \) is approximately \( 3.14 \) and \( \sqrt{12} \) is approximately \( 3.464 \), this statement is true.

Based on the evaluations, the true statements are:

- **√12 < 4**
- **√12 > π**

If you need to choose just one statement that is true, **√12 < 4** and **√12 > π** are both true, but in contexts where only one can be selected, typically the simpler one might be preferred. Thus:

The statement **√12 < 4** is true.