Question

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

6–√<2
6–√<2

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

0<4–√
0<4–√

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

8–√<5

Answer 1

Let’s evaluate each inequality one by one:

1. **6–√ < 2**
- \( \sqrt{6} \) is approximately 2.45, so \( 6 - \sqrt{6} \approx 6 - 2.45 = 3.55 \).
- Thus, \( 6 - \sqrt{6} < 2 \) is **false**.

2. **8–√ > 6–√**
- \( \sqrt{8} \) is approximately 2.83, and \( \sqrt{6} \) is approximately 2.45.
- Thus, \( \sqrt{8} > \sqrt{6} \) is **true**.

3. **0 < 4–√**
- \( \sqrt{4} = 2 \), so \( 0 < 2 \) is **true**.

4. **8–√ > 3**
- We've deemed \( \sqrt{8} \approx 2.83 \), which is not greater than 3. Thus, this statement is **false**.

5. **8–√ < 5**
- Since \( \sqrt{8} \approx 2.83 \), \( 2.83 < 5 \) is **true**.

Based on this evaluation, the correct inequalities are:

- **8–√ > 6–√**
- **0 < 4–√**
- **8–√ < 5**

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