To evaluate the inequalities provided, let's first calculate the square roots involved.
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\(\sqrt{8}\): \[ \sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2} \approx 2 \cdot 1.414 \approx 2.828 \]
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\(\sqrt{6}\): \[ \sqrt{6} \approx 2.449 \]
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\(\sqrt{2}\): \[ \sqrt{2} \approx 1.414 \]
Now we can evaluate each inequality:
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\(8 - \sqrt{8} > 3\): \[ 8 - 2.828 \approx 5.172 > 3 \quad \text{(True)} \]
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\(8 - \sqrt{8} > \sqrt{6}\): \[ 5.172 > 2.449 \quad \text{(True)} \]
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\(\sqrt{6} < 2\): \[ 2.449 < 2 \quad \text{(False)} \]
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\(\sqrt{6} < 2.8\): \[ 2.449 < 2.828 \quad \text{(True)} \]
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\(\sqrt{8} < 5\): \[ 2.828 < 5 \quad \text{(True)} \]
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\(0 < \sqrt{4}\): \[ 0 < 2 \quad \text{(True)} \]
Therefore, the correct statements from the list of inequalities that are true are:
- \(8 - \sqrt{8} > 3\)
- \(8 - \sqrt{8} > \sqrt{6}\)
- \(\sqrt{6} < 2.8\)
Thus, the three correct answers are:
- \(8 - \sqrt{8} > 3\)
- \(8 - \sqrt{8} > \sqrt{6}\)
- \(\sqrt{6} < 2.8\)