Why is the square root of 12 simplified by "4", and not "6" or "3"?

Question

So, my issue is understanding simplifying square roots. I heard people say "go with the highest number to simplify the root", but 6 is higher than "4", and then I hear, "go with the smallest number for simplicity like 3", instead, people go for "4". What is it I do not understand?

Answer 1

√12=√(2×2×3)=√(2×2)×√3=2√3. To simplify the square root of n, you are looking for the largest perfect square which is a factor of n. When n=12, the largest such factor is 4, because it’s the largest perfect square, whereas 3 and 6 are not perfect squares.