Explain the product and quotient properties of square roots and include examples.

Product property of square roots: 
For all positive real numbers a and b, the square root of the product is the same as the product of the square roots: 
√a * √b = √ab 
example: 
√3 * √2 = √(3 * 2) = √6 

Quotient property of square roots: 
For all positive real numbers a and b, b ≠ 0: the square root of the quotient is the same as the quotient of the square roots: 
√a / √b = √a/b 
example: 
√5 / √3 = √5/3