Question

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

0 < v4

v8 < 5

v8 > 3

v8 > v6

v6 < 2

Answer 1

To evaluate the inequalities involving square roots of numbers, let's analyze each one:

1. **0 < v4**:
- The square root of 4 is 2. Therefore, 0 < 2 is true.

2. **v8 < 5**:
- The square root of 8 is approximately 2.83. Thus, 2.83 < 5 is true.

3. **v8 > 3**:
- Given that v8 is approximately 2.83, the statement 2.83 > 3 is false.

4. **v8 > v6**:
- The square root of 8 (approximately 2.83) and the square root of 6 (approximately 2.45). Therefore, v8 > v6 is true since 2.83 > 2.45.

5. **v6 < 2**:
- Since v6 is approximately 2.45, the statement 2.45 < 2 is false.

Based on our analysis, the correct inequalities that are true are:

- 0 < v4
- v8 < 5
- v8 > v6

So the three correct answers are:

1. 0 < v4
2. v8 < 5
3. v8 > v6