Dear Hexin,

 Please consult

https://sites.math.rutgers.edu/~zeilberg/Hist21/q5S.pdf

for the full solutions.

You got 8 points (out of 10).

4(i) was right, but 4(ii) was utter nonsense. You  tried to "adapt" the proof that sqrt(2) is irrational, but what came out did not make sense.

 Best wishes,

   Dr. Z.