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