Then you have misunderstood the whole thing! The theorem you are trying to prove is that "If p is the not the square of an integer and then x is irrational". You cannot justchoosea value for x. x is "given" by . The crucial point here is "Assume that x is a positive rational number. What is thedefinitionof "rational number"?

Again, you cannotfor part 2 I let k = 1, x = 3/2 and showed that 1 < 3/2 < 2assumea value for x. x is given by and you must use that x.

For part 3 and 4 I have no idea what to do and i'm not sure whether i've done the prior correctly. I'd appreciate any help. Thanks!