Number Properties: how can n not be an integer if n^2 is?

[kimd6746]

Hello,

I have a question regarding squaring. I know that if the square root of any number always produces an integer, then that number must have been an integer to begin with. However, according to the OG answer explanations, n may or may not be an integer if n^2 is an integer. How can this be?


If √n is an integer, then n must be an integer as well. (understood)

If n^2 is an integer, n may or may not be an integer. (can someone show me/give me an example how n can be an integer or not an integer if n^2 produces an integer?)

Thanks,

[guest]

Here's an example and counter example.

(1) n=2, n^2 =4, both are integers.

(2) n=sqrt(2), n^2 =2, n is not an integer

[kimd6746]

OMG! How could I have not recognized this!!!! :oops: Thank you for your example!

[Guest]

It only gets worse from here. lol

[rfernandez]

Well done!