Question

:Prove by contradiction the irrationality of cube root of 2

Answer 1

Answer:

By contradiction, say 2–√3 is rational

then 2–√3=ab in the lowest form, where a,b∈Z,b≠0

2b3=a3

b3=a32

therefore, a3 is even

therefore, 2∣a3,

therefore, 2∣a

∃k∈Z,a=2k

sub in: 2b3=(2k)3

b3=4k3, therefore 2|b

Contradiction, a and b have common factor of two