To determine which statement is true using rational approximations, let's analyze each option:
A. \( \sqrt{49} < 7 \): This is false because \( \sqrt{49} = 7 \).
B. \( \sqrt{49} > 7 \): This is false since \( \sqrt{49} = 7 \).
C. \( \sqrt{48} < \sqrt{36} \): To evaluate this, we can observe that \( \sqrt{48} \) is approximately \( 6.93 \) (since \( \sqrt{49} = 7 \) and \( 48 \) is just under \( 49 \)), and \( \sqrt{36} = 6 \). Therefore, \( \sqrt{48} > \sqrt{36} \), making this statement false.
D. \( \sqrt{48} > \sqrt{36} \): Following the calculation from C, \( \sqrt{48} \approx 6.93 \) and \( \sqrt{36} = 6 \), which confirms that \( \sqrt{48} > \sqrt{36} \), making this statement true.
So the correct answer is D. \( \sqrt{48} > \sqrt{36} \).