Trigger warning: Here I will get fanciful and perhaps "recreational".
One of the convergents in the continued fraction expansion of $\sqrt 3$ is $\dfrac{71}{41}$ and so we get $$ 71^2 = 5041 \approx 5043 = 41^2 \times 3 $$ Similarly, with $\sqrt 2$ we get $$ 41^2 = 1681 \approx 1682 = 29^2 \times 2, $$ and the coincidental fact that $41$ appears early in among the convergents gives us: \begin{align} & 71^2\times 2 & = 10082 \\ \approx {} & 41^2\times 6 & = 10086 \\ \approx{} & 29^2 \times 12 & = 10092 \end{align} But I think proximity of these six small multiples of large squares is somewhat unusual: $$ \left. \begin{align} & 71^2\times 2 & = 10082 \\ \approx {} & 41^2\times 6 & = 10086 \\ \approx {} & 29^2 \times 12 = 58^2\times 3 & = 10092 \\ \approx {} & 38^2 \times 7 & = 10108 \\ \approx {} & 17^2 \times 35 & = 10115 \\ \approx {} & 45^2 \times 5 & = 10125 \end{align} \right\} \quad \text{range} = 43 $$ Might this "coincidence" either be an early convergent in some higher-dimensional analog of a continued fraction or might it otherwise be "explained"?