>No, sqrt(2) is exact and no approximation is needed -- it's the diagonal of a 1x1 square.
That's like saying that the goat-grass system as described is exact, and no approximation is needed. I can write 1 x sqrt(2) just as easily as I can write 1 x (goat-grass constant). We arbitrarily choose what constants and symbols are allowed when we use the phrase "exact solution." Philosophically, every solution is at most breaking down an answer into other solutions.
That's like saying that the goat-grass system as described is exact, and no approximation is needed. I can write 1 x sqrt(2) just as easily as I can write 1 x (goat-grass constant). We arbitrarily choose what constants and symbols are allowed when we use the phrase "exact solution." Philosophically, every solution is at most breaking down an answer into other solutions.