To evaluate the statements using rational approximations:
A. \( \sqrt{49} < 7 \)
- This statement is false because \( \sqrt{49} = 7 \).
B. \( \sqrt{49} > 7 \)
- This statement is also false for the same reason as above.
C. \( \sqrt{48} < \sqrt{36} \)
- We can find that \( \sqrt{36} = 6 \). \( \sqrt{48} \) can be approximated as between \( 6.9 \) and \( 7 \) since \( 48 \) is closer to \( 49 \) than to \( 36 \). Thus, \( \sqrt{48} > 6 \), making this statement false.
D. \( \sqrt{48} > \sqrt{36} \)
- Since \( \sqrt{36} = 6 \), we find \( \sqrt{48} \approx 6.93 \), which is greater than \( 6 \). Therefore, this statement is true.
The correct answer is: D. \( \sqrt{48} > \sqrt{36} \).
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