Numbers without square roots

Ok, I know this is slightly off-topic but here it is help me for two seconds and threads closed I promise.

I was studying the full mesh network equation which is n(n-1)/2=e (n =device number e = cables required for full mesh).

I realized (I'm an idiot btw) that as long as the number of devices has a square root or can be obtained by a number multipled by itself the number of cables required for full mesh will always be an even number.

Im probably wrong on the square root thing as well my math sucks, but what is the term for a number that can not be obtained by multiplying a number by itself?

5² = 25 thats a number with a square root right?
24 can't be obtained using ² so what would 24 called term wise?

Sorry for wasting everyones time

You might want to post that question in the Highly Technical Section of Anandtech.

Every integer can be obtained by squaring. It's just that some, like your example "24", have irrational roots. The sq root of 24 is an irrational number. But squaring that irrational number always = 24. You can test this using calc.exe. Raise 24 to the power of 0.5. Then square it. You're back to 24.

You want to know: what is the term for integers that have irrational square roots? I do not think they have their own name.