Square orchard short by 31 trees

A grower sets out young trees in a square grid and finds he has $146$ trees left over. To grow the square by one more row and one more column, he must buy another $31$ trees. How many trees stand in the completed, larger square?

$7921$. Going from an $n\times n$ square to $(n+1)\times(n+1)$ needs $2n+1$ extra trees, which here is $146+31=177$. So $n=88$ and the final square holds $89^2=7921$ trees.