Question

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

8–√>6–√
square root of 8 is greater than square root of 6

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

8–√<5
8–√<5

6–√<2
6–√<2

0<4–√

Answer 1

To evaluate the inequalities involving square roots, we can calculate the approximate values of the square roots:

1. **\(\sqrt{8} \approx 2.83\)**
2. **\(\sqrt{6} \approx 2.45\)**
3. **\(\sqrt{5} \approx 2.24\)**
4. **\(\sqrt{4} = 2\)**

Now, let's analyze each statement:

1. **\(\sqrt{8} > \sqrt{6}\)**:
- True, because \(2.83 > 2.45\).

2. **\(\sqrt{8} > 3\)**:
- False, because \(2.83 < 3\).

3. **\(\sqrt{8} < 5\)**:
- True, because \(2.83 < 5\).

4. **\(\sqrt{6} < 2\)**:
- False, because \(2.45 > 2\).

5. **\(0 < \sqrt{4}\)**:
- True, because \(\sqrt{4} = 2\), which is greater than 0.

Therefore, the correct true inequalities are:

- \(\sqrt{8} > \sqrt{6}\)
- \(\sqrt{8} < 5\)
- \(0 < \sqrt{4}\)

The three correct answers are:
- \(8–\sqrt{\,} > 6–\sqrt{\,}\)
- \(8–\sqrt{\,} < 5\)
- \(0 < 4–\sqrt{\,}\)