Two concentric circles are shown. If the area of the shaded region is equal to the area of the non-shaded region. what is the ratio of the radius of the larger circle to the radius of the smaler circle? Express your answer in simplest radical form.
small circle area = pi r^2 is equal to Large circle area (pi L^2) minus small circle area(pi r^2)
pi r^2 = pi L^2 - pi r^2
2 pi r2 = pi L2
2 r2 = L2
2 = L2 / r2
sqrt2 = L / r