To determine which of the inequalities are true, let's evaluate each one step by step.
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\( 6 - \sqrt{2} < 2 \)
- First, calculate \( \sqrt{2} \) which is approximately \( 1.414 \).
- Therefore, \( 6 - \sqrt{2} \approx 6 - 1.414 = 4.586 \).
- \( 4.586 < 2 \) is false.
-
\( 0 < 4 - \sqrt{4} \)
- Calculate \( \sqrt{4} = 2 \).
- Therefore, \( 4 - \sqrt{4} = 4 - 2 = 2 \).
- \( 0 < 2 \) is true.
-
\( \sqrt{8} < 5 \)
- Calculate \( \sqrt{8} \) which is approximately \( 2.828 \).
- \( 2.828 < 5 \) is true.
-
\( \sqrt{8} > 3 \)
- We already found \( \sqrt{8} \approx 2.828 \).
- \( 2.828 > 3 \) is false.
-
\( \sqrt{8} > \sqrt{6} \)
- Calculate \( \sqrt{6} \) which is approximately \( 2.449 \).
- Since \( 2.828 > 2.449 \), this is true.
Based on the evaluations above, the three correct true inequalities are:
- \( 0 < 4 - \sqrt{4} \)
- \( \sqrt{8} < 5 \)
- \( \sqrt{8} > \sqrt{6} \)
Therefore, the true inequalities are the second, third, and fifth responses.