To evaluate the statements, we will calculate the values of each expression.
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For statement A: \( \sqrt{12} > \pi \)
We can approximate \( \sqrt{12} \) as follows:
\( \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3} \).
\( \sqrt{3} \) is approximately \( 1.732 \), so:
\( 2\sqrt{3} \approx 2 \times 1.732 \approx 3.464 \).
We know that \( \pi \) is approximately \( 3.14159 \).
Hence, \( 3.464 > 3.14159 \) → \( \sqrt{12} > \pi \) is true. -
For statement B: \( \sqrt{16} > 4 \)
Here, \( \sqrt{16} = 4 \).
So, \( 4 > 4 \) is false. -
For statement C: \( \sqrt{12} < \pi \)
Since we determined that \( \sqrt{12} > \pi \) is true, this statement is false. -
For statement D: \( \sqrt{16} < 4 \)
Again, since \( \sqrt{16} = 4 \), the statement \( 4 < 4 \) is false.
Thus, the only statement that is true is A: \( \sqrt{12} > \pi \).
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