What is the geometric mean of 4 and 12?

• A. $\sqrt{48}$
• B. $8$
• C. $\frac{12}{4}$
• D. $\frac{4+12}{2}$

Answer: (A)

Verified step by step guidance

1. Understand that the geometric mean of two numbers is the square root of their product. It is a type of average that is especially useful when dealing with rates or multiplicative processes.
2. Identify the two numbers given: 4 and 12.
3. Calculate the product of the two numbers: multiply 4 by 12, which gives \$4 \times 12$.
4. Take the square root of the product to find the geometric mean: \(\sqrt{4 \times 12}\).
5. Simplify the square root expression if possible to express the geometric mean in simplest form.