To evaluate the statements using rational approximations, we first need to calculate the values of the square roots involved.
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Calculate \( \sqrt{48} \): \[ \sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3} \approx 4 \times 1.732 = 6.928 \text{ (approx)} \]
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Calculate \( \sqrt{49} \): \[ \sqrt{49} = 7 \]
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Calculate \( \sqrt{36} \): \[ \sqrt{36} = 6 \]
Now, we will evaluate each of the statements:
A. \( \sqrt{48} \leq 7 \)
From our approximation, \( 6.928 \leq 7 \) is true.
B. \( \sqrt{49} \geq 7 \)
Since \( \sqrt{49} = 7 \), it is also true that \( 7 \geq 7 \).
C. \( \sqrt{48} \leq \sqrt{36} \)
From our calculations, \( 6.928 \leq 6 \) is false.
D. \( \sqrt{48} \geq \sqrt{36} \)
Since \( 6.928 \geq 6 \) is true.
Summary of Findings:
- Statement A is true.
- Statement B is true.
- Statement C is false.
- Statement D is true.
Thus, the true statements are A, B, and D.
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