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?

Question

My question is fairly straight forward. 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? 

 

Answer 1

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.