Clever Approximation #2

Algebra Level 5

$\large \left\lfloor \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}} + \cdots + \frac{1}{\sqrt{992016}}\right\rfloor = \, ?$

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