Question

The area of a square garden is 128m sqared.how long is the diagonal

Answer 1

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 . 

Answer 2

The length will be the square root of 128.  Factoring out a 64, this is 8sqrt(2).  To find the diagonal of square, multiply the length by sqrt(2), for a result of 8sqrt(2)*sqrt(2)=8*2=16.