Question

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

8–√>3
square root of 8 is greater than 3

6–√<2
6–√<2

0<4–√
0<4–√

8–√<5
8–√<5

8–√>6–√

Answer 1

Let's evaluate each inequality one by one.

1. **8–√ > 3**: This means \(\sqrt{8} > 3\). Since \(\sqrt{8} \approx 2.83\), this inequality is **false**.

2. **6–√ < 2**: This means \(\sqrt{6} < 2\). Since \(\sqrt{6} \approx 2.45\), this inequality is **false**.

3. **0 < 4–√**: This means \(0 < \sqrt{4}\). Since \(\sqrt{4} = 2\), this inequality is **true**.

4. **8–√ < 5**: This means \(\sqrt{8} < 5\). Since \(\sqrt{8} \approx 2.83\), this inequality is **true**.

5. **8–√ > 6–√**: This means \(\sqrt{8} > \sqrt{6}\). Since \(\sqrt{8} \approx 2.83\) and \(\sqrt{6} \approx 2.45\), this inequality is **true**.

So the three correct answers are:
- \(0 < 4–√\)
- \(8–√ < 5\)
- \(8–√ > 6–√\)