Question

proveROOT 3 ARE IRRATIONAL

Answer 1

I hope it helps your

Answer 2

let us assume to the contrary that root 3 is irrational.
we can find integers a and b such that root 3 =a/b
a and b have a common factor other than 1
than we can find common factor
assume that a and b are coprime.

so, b root 3
squaring on both sides
we get 3B2 =a2

a2 is divisible by 3
it follows that a is also divisible by 3

a =3c for some integers c
substituting for a
3b2 =9c
b2=3c2

this means that b2 is divisible by 3
so b is also divisible by 3

a and b have at least 3 as a common factor
but this contradicts the fact that a and b are coprime.
this contradiction has arisen because of our incorrect assumption that root 3 is rational so we conclude that root 3 is irrational.

hope it helps you