Finding $\sqrt{625}$ without a calculator We were factoring $25n^2+15n-4$ in class and my professor used the quadratic formula. This root came up and he wrote the answer directly. He doesn't want us to use calculators. 
Is there any trick for this?

I guess your professor has been using the following trick: the square of a number of the form $10n + 5$ is $100n(n+1) + 25$. Indeed $(10n + 5)^2 = 100n^2 + 100n + 25 = 100n(n+1) + 25$.
For instance:
\begin{align}
n &= 0: && 5^2 = 25 &&\text{since $0 \times 1 = 0$} \\
n &= 1: && 15^2 = 225 &&\text{since $1 \times 2 = 2$} \\
n &= 2: && 25^2 = 625 &&\text{since $2 \times 3 = 6$} \\
n &= 3: && 35^2 = 1225 &&\text{since $3 \times 4 = 12$} \\
n &= 4: && 45^2 = 2025 &&\text{since $4 \times 5 = 20$} \\
n &= 5: && 55^2 = 3025 &&\text{since $5 \times 6 = 30$} \\
&\ \vdots
\end{align}
If you know this trick, it is not difficult to remember that $25^2 = 625$...
