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 $\lfloor \sqrt{1}\rfloor +\lfloor \sqrt{2}\rfloor +\lfloor \sqrt{3}\rfloor +\cdots +\lfloor \sqrt{25}\rfloor$.