1536 is not a perfect square, but has an irrational square root
of about 39.19.  Therefore it is not a perfect square and so it 
is impossible to have a square array with 1536 soldiers.  The 
closest larger perfect square to 1536 is 40² or 1600. So 
1600-1536 or 64 soldiers are needed. 

There will be 40 soldiers on each side of the square, so there
will be 1 less space between soldiers on each side of the square
than there are soldiers on each side.  So there are 39 2-meter
spaces between soldiers, so each side will be 39×2 or 78 meters
long.  So the area of the square will be 78² or 6084 square 
meters.

Edwin