Question

prove that 1 upon root 2 is irrational


answer the neat and clean

Answer 1

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

Answer 2

here is ur answer in image


hope it helps u a lot