Question 7
The symbolism $\lfloor x \rfloor$ denotes the largest integer not exceeding $x.$ For example, $\lfloor 3 \rfloor = 3,$ and $\lfloor \frac{9}{2} \rfloor = 4.$ Compute $$
\begin{gathered} \lfloor \sqrt{1} \rfloor + \lfloor \sqrt{2} \rfloor + \lfloor \sqrt{3} \rfloor \\ {}+ \cdots + \lfloor \sqrt{16} \rfloor. \end{gathered}
$$
\begin{gathered} \lfloor \sqrt{1} \rfloor + \lfloor \sqrt{2} \rfloor + \lfloor \sqrt{3} \rfloor \\ {}+ \cdots + \lfloor \sqrt{16} \rfloor. \end{gathered}
$$