a. When v = c, then v^2 = c^2. The fraction v^2/c^2 becomes 1. The inside of the root is 1 - 1 which equals zero. Square root of zero is zero, and zero times L0, no matter what value L0 has, is zero. Therefore, when v = c, the left side equals zero.
b. When v = 0, and c is positive, v/c = v^2/c^2 = 0. By subtracting v^2/c^2, which is zero for v = 0, from 1, you get 1. Square root of 1 is 1. Then you multiply that by L0 to get L0. The greatest possible value of the left expression is L0.