Using rational approximations, what statement is true?

Question

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.