AMC 10B 2003 Problem 7

The symbolism \lfloor x\rfloor denotes the largest integer not exceeding x. For example, \lfloor 3\rfloor=3, and \lfloor 9 / 2\rfloor=4. Compute

\lfloor\sqrt{1}\rfloor+\lfloor\sqrt{2}\rfloor+\lfloor\sqrt{3}\rfloor+\cdots+\lfloor\sqrt{16}\rfloor .

Answer Choices
A. 35
B. 38
C. 40
D. 42
E. 136