Ordering Square Root Differences

Note that each difference is of the form $\sqrt{x+8} - \sqrt{x} = \frac{8}{\sqrt{x+8} + \sqrt{x}}$. As $x$ increases, the denominator increases, so the value decreases. Values of $x$ for A, B, C, D are 51, 29, 79, 71 respectively. Since $29 < 51 < 71 < 79$, we have $B > A > D > C$. In increasing order: $C < D < A < B$.