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–√<5
8–√<5

8–√>3

Answer 1

To determine which inequalities are true, we'll evaluate each one:

1. **\( 6 - \sqrt{2} < 2 \)**:
- Calculating \( \sqrt{2} \) gives approximately 1.414.
- Therefore, \( 6 - \sqrt{2} \approx 6 - 1.414 \approx 4.586 \).
- Since \( 4.586 < 2 \) is false, this inequality is **not true**.

2. **\( \sqrt{8} > \sqrt{6} \)**:
- Calculating \( \sqrt{8} \approx 2.828 \) and \( \sqrt{6} \approx 2.449 \).
- Since \( 2.828 > 2.449 \) is true, this inequality is **true**.

3. **\( 0 < \sqrt{4} \)**:
- Since \( \sqrt{4} = 2 \), the inequality \( 0 < 2 \) is true. Thus, this inequality is **true**.

4. **\( \sqrt{8} < 5 \)**:
- We've already calculated \( \sqrt{8} \approx 2.828 \).
- Since \( 2.828 < 5 \) is true, this inequality is **true**.

5. **\( \sqrt{8} > 3 \)**:
- We know \( \sqrt{8} \approx 2.828 \) and since \( 2.828 \) is not greater than \( 3 \), this inequality is **not true**.

The three correct inequalities are:

1. \( \sqrt{8} > \sqrt{6} \)
2. \( 0 < \sqrt{4} \)
3. \( \sqrt{8} < 5 \)