Question

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

6–√<2
6√<2

8√<5
8–√<5

0<4–√
0<4–√

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

8√>3

Answer 1

To determine which inequalities are true, let's evaluate each one step by step.

1. **6 - √ < 2**:
- Approximate √ (square root of 6) ≈ 2.45, so 6 - 2.45 ≈ 3.55.
- Thus, 3.55 < 2 is **false**.

2. **6√ < 2**:
- This is generally interpreted as \(6 \times \sqrt{}\), and since \(6\) multiplied by any positive number is greater than \(2\), this is **false**.

3. **8√ < 5**:
- Again, assuming this is \(8 \times \sqrt{}\), \(8\) multiplied by any positive number will also be greater than \(5\), so this is **false**.

4. **8 - √ < 5**:
- Approximate √ (square root of 8) ≈ 2.83, so 8 - 2.83 ≈ 5.17, thus 5.17 < 5 is **false**.

5. **0 < 4 - √**:
- Assuming √ refers to \(√4\) or simply \(2\), we have \(4 - 2 = 2\). Since \(0 < 2\), this is **true**.

6. **8 - √ > 6 - √**:
- Approximate √ (square root of 8) ≈ 2.83 and √ (square root of 6) ≈ 2.45
- Then 8 - 2.83 = 5.17 and 6 - 2.45 = 3.55, so 5.17 > 3.55 is **true**.

7. **8√ > 3**:
- Assuming this means \(8 \times \sqrt{}\), and since \(8\) is a positive number, this is generally **true** for positive values under the square root.

Therefore, the three correct answers are:
- **0 < 4 - √**
- **8 - √ > 6 - √**
- **8√ > 3**