To evaluate the given statements, let's calculate the values of the square roots and \(\pi\) as needed:
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Statement A: \(\sqrt{16} > \sqrt{4}\)
- \(\sqrt{16} = 4\)
- \(\sqrt{4} = 2\)
- Therefore, \(4 > 2\) is true.
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Statement B: \(\sqrt{12} > \pi\)
- \(\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}\)
- The approximate value of \(\sqrt{3} \approx 1.732\), hence \(2\sqrt{3} \approx 3.464\).
- The approximate value of \(\pi \approx 3.14159\).
- Therefore, \(3.464 > 3.14159\) is true.
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Statement C: \(\sqrt{16} < 4\)
- We already established that \(\sqrt{16} = 4\).
- Thus, \(4 < 4\) is false.
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Statement D: \(\sqrt{12} < \pi\)
- We found that \(\sqrt{12} \approx 3.464\) and \(\pi \approx 3.14159\).
- Therefore, \(3.464 < 3.14159\) is false.
From this evaluation:
- Statements A and B are true.
- Statements C and D are false.
The true statements are A: \(\sqrt{16} > \sqrt{4}\) and B: \(\sqrt{12} > \pi\).