We will prove it by the method of contradiction. 

Let 1/√2 is a rational number

So  we can write 1/√2 = a/b .........1

where a and b are relatively prime numbers.

Squaring equation 1 on bothe side,

(1/√2)² = (a/b)²

=> 1/2 = a² /b²

=> 2a² = b²

So b² is an even number

=> b must be an even number

Let b = 2c

On squaring both side,

=> b² = (2c)²

=> b² = 4c²

now from equation 1

2a² = 4c²

=> a² = 2c²

=> a must be an even number.

Now since both a and b are even numbers, then a and b can not be relatively prime.

So our assumption is wrong.

Hense 1/√2 is an irrational number.