Find $\sqrt{n}$

We note that the LHS is the sum of a arithmetic progression with $n$ terms, first term $a_1=2$ and common difference $d=3$ . Therefore, the last term $a_n = 2 + 3(n-1) = 3n-1$ and we have:

$\begin{aligned} \color{#3D99F6}{\underbrace{2}_{a_1} + 5 + 8 + 11 + \cdots + \underbrace{(3n-1)}_{a_n}} & = 950 & \small \color{#3D99F6}{\text{Sum of AP }S = \frac {n(a_1+a_n)}2} \\ \implies \frac {n(2+3n-1)}2 & = 950 \\ 3n^2 + n & = 1900 \\ 3n^2 + n - 1900 & = 0 \\ (3n+76)(n-25) & = 0 \\ \implies n & = 25 & \small \color{#3D99F6}{n \text{ must be a positive integer}} \\ \implies \sqrt n & = \boxed{5} \end{aligned}$