2 √2 = 2 * 2^(1/2) = 2^(3/2), so we can rewrite item II:

(2 √2)^35 = (2^3/2)^35 = 2^105/2

and since 105/2 < 60, this is less than 2^60.

To compare 2^60 and 3^42, we can notice that 2^60 = (2^3)^20 = 8^20, and 3^42 = (3^2)^21 = 9^21, and since 8^20 has both a smaller base and smaller exponent than 9^21, it is the smaller number (here using the fact that the bases are positive integers), so the answer is II, I, III.