To find the length of the diagonal of a square given the side length, we use the formula:
\[ \text{Diagonal} = \text{side} \times \sqrt{2} \]
Given that the side length of the square park is 700 feet, we can substitute that into the formula:
\[ \text{Diagonal} = 700 \times \sqrt{2} \]
Using the approximation given for \(\sqrt{2}\), which is 1.4:
\[ \text{Diagonal} = 700 \times 1.4 \]
Now, we can perform the multiplication:
\[ \text{Diagonal} = 980 \]
Therefore, the approximate length from one corner to the opposite corner of the square park is
\[ \boxed{980} \text{ feet.} \]