Proof: For every natural n, prove sqrt(n) is integer or...

[vikramtiwari]

For every n E N, prove either sqrt(n) is an integer or irrational??

I don't really understand the problem. Since we know that sqrt(4) is an integer but sqrt(5) is an irrational number.....and still 4 and 5 both are natural numbers 'N'..

 

[royhaas]

If an integer is not a perfect square, assume its square root is rational and obtain a contradiction.

 

[pka]

Here is one proof.