We start with an x by x sheet of cardboard like this:

 

then we mark off 11x11 squares to cut out of 
the corners, leaving x-22 for the widths of 
the four sides to be folded up.



Now lets cut them out:



Draw in the square base:




So the length and the width will both be
(x-22) and the height will be 11. So the 
volume will be

V = lwh = (x-22)(x-22)(11) = 11(x-22)²

Now we set this = 704

11(x-22)² = 704

Divide both sides by 11

  (x-22)² = 64

Using the square root principle:

   x - 22 = 8

        x = 30

So we needed a 30x30 piece of cardboard.

Edwin