Question

Prove that 1/2√2 is an irrational number

Answer 1

we know that , root 2 is a irrational number.
let 1/2 root 2 is a rational number.
1/2 root 2 = p/q ( where q is not equal to 0 and p , q are co primes )
root 2 = 2p / q
this is a contradiction.
if left hand side is irrational number then right hand side is also irrational number.
our assumption is wrong . 1/2 root 2 is a irrational number.