Question

Which inequalities are true? Select the three correct answers.(3 points)
Responses

9–√<12−−√
9–√<12−−√

6–√<2–√
6–√<2–√

8–√>8
square root of 8 is greater than 8

8–√>2
square root of 8 is greater than 2

0<5–√

Answer 1

To determine the truth of each inequality, we will evaluate each one step by step.

1. **\( \sqrt{9} < \sqrt{12} \)**:
- \( \sqrt{9} = 3 \) and \( \sqrt{12} \approx 3.464 \).
- True: \( 3 < 3.464 \).

2. **\( \sqrt{6} < \sqrt{2} \)**:
- \( \sqrt{6} \approx 2.449 \) and \( \sqrt{2} \approx 1.414 \).
- False: \( 2.449 > 1.414 \).

3. **\( \sqrt{8} > 8 \)**:
- \( \sqrt{8} \approx 2.828 \) which is not greater than 8.
- False: \( 2.828 < 8 \).

4. **\( \sqrt{8} > 2 \)**:
- \( \sqrt{8} \approx 2.828 \).
- True: \( 2.828 > 2 \).

5. **\( 0 < \sqrt{5} \)**:
- \( \sqrt{5} \approx 2.236 \).
- True: \( 0 < 2.236 \).

Based on these evaluations, the three true inequalities are:

- \( \sqrt{9} < \sqrt{12} \)
- \( \sqrt{8} > 2 \)
- \( 0 < \sqrt{5} \)

So, the correct answers are:
1. \( \sqrt{9} < \sqrt{12} \)
2. \( \sqrt{8} > 2 \)
3. \( 0 < \sqrt{5} \)