I like how in the OG explanations it will say things like "Since, we know that the square root of 2601 is 51, we just plug it in to so and so." This does not seem like common knowledge.
I agree! However, I do advise my students to at least recognize the perfect squares up to 20. One tip is, if you see that it would be helpful to have a perfect square for your constant, try factoring the constant down to see whether it is a perfect square.