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.