What is greatest integer function?

Algebra Level 4

$\large \lfloor \sqrt{1} \rfloor + \lfloor \sqrt{2} \rfloor + \lfloor \sqrt{3} \rfloor + \cdots + \lfloor \sqrt{2004} \rfloor =\, ?$

Notation: $\lfloor \cdot \rfloor$ denotes the floor function.