Explanation

Let the value be L = sqrt(4 + sqrt(4 - sqrt(4 + ...))) with alternating signs. Put L = sqrt(4 + Y) with Y = sqrt(4 - L); then L^2 = 4 + sqrt(4 - L), so (L^2 - 4)^2 = 4 - L, i.e. L^4 - 8L^2 + L + 12 = (L^2 - L - 3)(L^2 + L - 4) = 0. With L > 2 the admissible root is L = (1 + sqrt(13))/2 = 2.30 (the iteration converges to it). Hence option (c).