What is the restriction on the rule that says, when two numbers are multiplied within a square root, you can split it into a multiplication of two square roots?

As long as you're not dealing with negative numbers, you can always split a root of a product into the product of roots.√ (6) = √ (2) * √ (3) √ (75) = √ (25) * √ (3) √ (210) = √ (2) * √ (3) * √ (5) * √ (7) √ (3xy) = √ (3) * √ (x) * √ (y) etc.