Question

Using rational approximations, what statement is true? (1 point)
• V12 <

• V12 > 1

• V16 > 4

• V16 < 4

Answer 1

To evaluate the statements regarding the values of \( \sqrt{12} \) and \( \sqrt{16} \):

1. **Calculating \( \sqrt{12} \)**:
- \( \sqrt{12} \) can be simplified as \( \sqrt{4 \times 3} = 2\sqrt{3} \).
- The approximate value of \( \sqrt{3} \) is about 1.732.
- Therefore, \( \sqrt{12} \approx 2 \times 1.732 = 3.464 \).
- This means \( \sqrt{12} < 4 \) and \( \sqrt{12} > 1 \).

2. **Calculating \( \sqrt{16} \)**:
- \( \sqrt{16} = 4 \).
- This indicates that \( \sqrt{16} = 4 \) and thus does not hold for \( \sqrt{16} > 4 \) or \( \sqrt{16} < 4 \).

Based on the evaluations:
- The statement **\( \sqrt{12} < 4 \)** is true, and so is \( \sqrt{12} > 1\).
- Therefore the true statements among the options are:
- \( \sqrt{12} > 1 \)
- \( \sqrt{16} = 4 \) (not listed).

Thus, the correct option from the provided choices would be **\( \sqrt{12} > 1 \)** (not listed among your given choices) or \( \sqrt{16} = 4\) (also not given); however, it is prudent to mention that out of the choices, the most verifiable are \( V12 > 1 \) and not one of the listed.

For the current choices provided, the only statement that can undeniably hold is:

- **\( V12 > 1 \)**