Question

Without plotting these numbers, decide which inequalities are true. Check all that apply.
StartRoot 7 EndRoot > 2
StartRoot 7 EndRoot < 7
StartRoot 7 EndRoot < StartRoot 8 EndRoot
StartRoot 8 EndRoot < 2
StartRoot 8 EndRoot < 8

Answer 1

To evaluate the given inequalities involving square roots, let's break them down one by one:

1. **\(\sqrt{7} > 2\)**:
- The value of \(\sqrt{7}\) is approximately 2.64575131, which is greater than 2.
- **True**.

2. **\(\sqrt{7} < 7\)**:
- The value of \(\sqrt{7}\) is approximately 2.64575131, which is clearly less than 7.
- **True**.

3. **\(\sqrt{7} < \sqrt{8}\)**:
- The value of \(\sqrt{8}\) is approximately 2.82842712, and since \(\sqrt{7} \approx 2.64575131\), it is indeed less than \(\sqrt{8}\).
- **True**.

4. **\(\sqrt{8} < 2\)**:
- Since \(\sqrt{8} \approx 2.82842712\), it is not less than 2.
- **False**.

5. **\(\sqrt{8} < 8\)**:
- The value of \(\sqrt{8} \approx 2.82842712\), which is definitely less than 8.
- **True**.

**True inequalities**: 1, 2, 3, and 5.