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. \(\sqrt{6} < 2.8\)