The area of a square is (side)².
If the area is 128m², then the side is (√128) meters. (That's 8√2.)
The diagonal is the hypotenuse of the right triangle you get
if you slice the square in half along the diagonal. Its length is
given in the words of Old Pythagoras:
c² = a² + b²
'a' and 'b' are sides of the square, so
c² = (√128)² + (√128)²
= 2 (√128)²
c = √ (2 x 128) = √256 = 16 meters .