Problem: Compute $\sqrt{(31)(30)(29)(28)+1}$. Solution: Let $k = 30$. We are trying to find $\sqrt{k(k+1)(k-1)(k-2)+1}$. Indeed, this is $ \sqrt{(k^2-2k)(k^2-1)+1} = \sqrt{k^{4}-2k^3-k^2+2k+1} = \sqrt{(k^2-k-1)^2} = 869 .$