What is the product of √a and √b?

What is the product of √a and √b?

• A. √a + b
• B. √(a + b)
• C. √a x b
• D. √(a x b)

Answer: (D)

The product of √a and √b is expressed mathematically as √a × √b. A key property of square roots states that the product of the square roots of two numbers is equal to the square root of the product of those two numbers. Specifically, it can be represented as: √a × √b = √(a × b). Thus, when taking the product of √a and √b, the correct representation is indeed √(a × b). This principle stems from the laws of exponents and the definitions of square roots. Understanding this property is essential because it simplifies calculations involving square roots in algebraic expressions.

The product of √a and √b is expressed mathematically as √a × √b. A key property of square roots states that the product of the square roots of two numbers is equal to the square root of the product of those two numbers. Specifically, it can be represented as:

√a × √b = √(a × b).

Thus, when taking the product of √a and √b, the correct representation is indeed √(a × b). This principle stems from the laws of exponents and the definitions of square roots. Understanding this property is essential because it simplifies calculations involving square roots in algebraic expressions.