To determine which inequalities are true, let's evaluate each option:
A. \(\sqrt{6} < 2\)
- Since \(\sqrt{4} = 2\) and \(\sqrt{6} \approx 2.45\), this inequality is false.
B. \(\sqrt{8} > 3\)
- \(\sqrt{8} \approx 2.83\), which is not greater than 3. Therefore, this inequality is false.
C. \(\sqrt{8} < 5\)
- Since \(\sqrt{8} \approx 2.83\), this inequality is true.
D. \(\sqrt{8} > \sqrt{6}\)
- We have \(\sqrt{8} \approx 2.83\) and \(\sqrt{6} \approx 2.45\). Since \(2.83 > 2.45\), this inequality is true.
E. \(0 < \sqrt{4}\)
- \(\sqrt{4} = 2\), thus \(0 < 2\) is true.
The three correct inequalities are:
- C. \(\sqrt{8} < 5\)
- D. \(\sqrt{8} > \sqrt{6}\)
- E. \(0 < \sqrt{4}\)
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