Question

prove root 2 be an irrational number

Answer 1

Let √2 be a rational number.Then√2=a/b,where a and b are co primes,and b≠0.
2=a²/b²...............(squaring both sides)
2b²=a²
⇒2 divides a.............(1)
let 2c=a.for any integer c
Substituting for a, we get 4c²=2b²
⇒2c²=b²
⇒2 divides b....................(2)
from(1) and (2) we get that 2 is a common factor of a and b.
This contradicts our assumption that a and b are co primes.
therefore √2 is irrational.