Question

prove that the square root of 2 is an irrational number

Answer 1

let us assume to the contrary root 2 is irrational
let a , b be integer with common factor 1 
root2 =a/b
a= b*root2 
by squaring on both sides
2b square =a square
=>b square =a  (1)
 since 2 divides a square 
2 divides a
we can write a =2c ,c is some integer (2)
there fore we can write 
2 b square = 4 c square 
2 divides b square 
therefore , 2divides b
ie a and b have 2 as common factor 
therefore our assumption is wrong
hence root 2 is irrational