John and Betty tried and tried to find the right number for the side length so the area of the square was three square metres but no whole numbers and no fractions worked . They sat down with their heads in their hands. They were both totally discouraged. "There must be a some length that can give us the right side length," huffed John. "But there aren't any whole numbers and there aren't any fractions. It's as though we'd have to make the number up if we wanted it to work."