Food for thought

Evaluate the sum $\frac{1}{\sqrt{1} + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \dotsb + \frac{1}{\sqrt{15} + \sqrt{16}}.$
Things like $\sqrt{5}+\sqrt{6}$ make me think of the difference of two squares….