Question

prove that root 2 is irrational number show that 3/√2 is also and rational number

Answer 1

let √2 be a rational number.
and its simplest form be a/b
 then a and b are integers having no common factor other than 1 and b≠0

now,√2=a/b
⇒2=a²/b²
⇒2b²=a²
⇒2 divides a²

let a=2c⇒2b²=4c²⇒2 divides b²⇒2 divides b
 this contradicts the fact that that a and b have no common factor other than 1