system
Given the following post, respond as if you're commenting on Reddit:
human
Proof: √p is irrational if p is a prime

This is my proof 

>Let p be a prime   
>  
>For the sake of contradiction suppose  √ p is rational   
>  
>Then  √ p = m/n ; m, n **∈ |N**  
>  
>p = (m/n) ²    
>  
>Since p is an integer, (m/n) ²  is an integer  
>  
>Then (m/n) is an integer  
>  
>This implies p = r \* r where r = m/n  
>  
>This implies p is divisible by r  
>  
>Contradiction  
>  
>Hence  √ p is irrational 

This is the proof I came up with, however the other proofs I found online are quite different. I would like to know if my way is correct and rigorous enough.

Appreciate your time. Thanks in advance.
gpt
If you think through it in detail, it turns out your proof is a bit circular.

When you say that if (m/n)^(2) is an integer, then m/n is an integer, you are relying on the fact that the square root of an integer is either an integer or an irrational number. But, if you're willing to use that as something established, then why go through all the hoops, instead of simply saying that no prime is a perfect square, and therefore the square root of a prime has to be irrational?

If you're not willing to use the fact that the square of an integer is either an integer or irrational, then you have to restructure your proof.