Question

Prove that root 3 is irrational.

Answer 1

hope it help pls mark me as brainlist

Answer 2

Let us assume that √3 is irrational

let, √3=a/b. {where a and b are integers and b≠0}

=>3=a²/b²

=>a²=3b²

a² is divisible by 3
a is also divisible by 3

Again,

Let a=3c

=>a²=(3c²) {squaring both side}

=>3b²=6c²

=>b²=3c²

b² is divisible by 3
b is also divisible by 3

Therefore ,both a and b have common factor of 3

So, This contradict the fact that our assumption is incorrect

Therefore, √3 is irrational