Square roots are not some "mathematical trivia", they're amongst the most fundamental operations in mathematics.

In arithmetic. There is a lot more to math than arithmetic.

Square roots are fundamental to (real and complex) analysis and to algebra (in the study of polynomials), so the two major branches of modern mathematics.

They are fundamental to the arithmetic used in analysis and algebra.

One can get along quite well without them once you replace the arithmetic expressions with more general objects.

Just come on. The square root of 2 is the easiest example of an irrational number, this has been known since Ancient Greece. You can't compute distances in Euclidean spaces without the square root. "Solving equations by roots" is the bread and butter of algebra. Adjoining roots to a field is how you get Galois Theory. Several algorithms related to number theory have complexity O(sqrt(n)). And so on.

You chose an extremely poor example and now you're trying to die on that hill. Please don't die on that hill.

Also fundamental to geometry (pythagorean equation and others).

Strangely enough, you'd be hard pressed to find a mathematician who doesn't know what a square root is.

And I didn't mention genetics. Nature is complicated.

You'd also be hard pressed to find one who doesn't know how to flush a toilet.

Neither trivia has anything to do with being good at mathematics as done by mathematicians.

Are you an LLM? You brought up the point of mathematicians not knowing what a square root is yourself. Anyway, the square root is is so many levels below maths as done by mathematicians, it's laughable.

It certainly is suspicious that their name starts, "llm"

Pretty sure you followed the thread wrong. They only mentioned the square root in response to you?