Between which two integers does $\sqrt{2017}$ fall? Between which two integers does $\sqrt{2017}$ fall? 


Since $2017$ is a prime, there's not much I can do with it. However, $2016$ (the number before it) and $2018$ (the one after) are not, so I tried to factorise them. But that didn't work so well either, because they too are not perfect squares, so if I multiply them by a number to make them perfect squares, they're no longer close to $2017.$ How can I solve this problem?

Update:
Okay, since $40^2 = 1600$ and $50^2 = 2500$, I just tried $45$ and $44$ and they happened to be the answer - but I want to be more mathematical than that...
$\sqrt{2017}\approx\sqrt{2000}=20\sqrt{5}\approx 20\cdot 2.236 \approx 45$ and
$$44^2 = 1936,\qquad 45^2=2025$$
hence $\sqrt{2017}\in\color{red}{\left(44,45\right)}$.
$\sqrt{1600} = 40$ and $\sqrt{2500} = 50$. $(40+4)^2 = 40^2 + 8\cdot 40 + 16 = 1936$ and $(40+5)^2 = 40^2 + 10\cdot 40 +25 = 2025$. Hence the desired answer is $44$ and $45$.