What is the minimum number of square marbles required to tile a floor of length 5 meters 78 cm and width 3 meters 74 cm?

5.78 meters x 3.28084 feet per meter = 18.96 feet

3.74 meters x 3.28084 feet per meter = 12.27 feet

I'd probably ignore the extra .02 feet on the width (= 1/4 inch) and call it 12.25 feet. Since you can theoretically get four three-inch-wide pieces (.25 ft = 3 in.) from each square foot tile, you'd need at the absolute minimum:

19 x 12 ft 3 in. = 233 one foot squares of tile

However, you should assume that some of the tiles will get broken during cutting or installation, so I suggest you buy a few more, especially if you're buying from a place that allows returns.

I'd get 240