Question

Which inequalities are true? Select the three correct answers.(3 points)Responses8–√>3square root of 8 is greater than 38–√>6–√square root of 8 is greater than square root of 66–√<26–√<28–√<58–√<50<4–√

Answer 1

To evaluate the inequalities provided, let's first calculate the square roots involved.

1. **\(\sqrt{8}\)**:
\[
\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2} \approx 2 \cdot 1.414 \approx 2.828
\]

2. **\(\sqrt{6}\)**:
\[
\sqrt{6} \approx 2.449
\]

3. **\(\sqrt{2}\)**:
\[
\sqrt{2} \approx 1.414
\]

Now we can evaluate each inequality:

1. **\(8 - \sqrt{8} > 3\)**:
\[
8 - 2.828 \approx 5.172 > 3 \quad \text{(True)}
\]

2. **\(8 - \sqrt{8} > \sqrt{6}\)**:
\[
5.172 > 2.449 \quad \text{(True)}
\]

3. **\(\sqrt{6} < 2\)**:
\[
2.449 < 2 \quad \text{(False)}
\]

4. **\(\sqrt{6} < 2.8\)**:
\[
2.449 < 2.828 \quad \text{(True)}
\]

5. **\(\sqrt{8} < 5\)**:
\[
2.828 < 5 \quad \text{(True)}
\]

6. **\(0 < \sqrt{4}\)**:
\[
0 < 2 \quad \text{(True)}
\]

Therefore, the correct statements from the list of inequalities that are true are:

1. \(8 - \sqrt{8} > 3\)
2. \(8 - \sqrt{8} > \sqrt{6}\)
3. \(\sqrt{6} < 2.8\)

Thus, the three correct answers are:

1. \(8 - \sqrt{8} > 3\)
2. \(8 - \sqrt{8} > \sqrt{6}\)
3. \(\sqrt{6} < 2.8\)