Question

prove that 3-5root 2 is irrational​

Answer 1

let us assume, to contrary,that 3-5√2 is rational

i.e. , we can find co prime a and b (b≠0) such that 3-5√2=a/b

therefore, 3-a/b=5√2

rearranging this equation we get 5√2=3-a/b

since a and b are integers ,we get 3-a/b is rational , and so 5√2is rational

but it contradicts the fact that 5√2 is irrational.

this contradiction has arisen because of our incorrect assumption that 3-5√2 is rational.

so, we conclude that 3-5√2 is irrational