What is the geometric mean of 4 and 12?

• A. $\frac{12}{4}$
• B. $\sqrt{16}$
• C. $\frac{4+12}{2}$
• D. $\sqrt{48}$

Answer: (D)

Verified step by step guidance

1. Understand that the geometric mean of two numbers, say \(a\) and \(b\), is defined as the square root of their product. Mathematically, it is given by \(\sqrt{a \times b}\).
2. Identify the two numbers given in the problem: 4 and 12.
3. Calculate the product of the two numbers: multiply 4 by 12 to get \$4 \times 12$.
4. Take the square root of the product obtained in the previous step. This means you compute \(\sqrt{4 \times 12}\).
5. Simplify the square root expression if possible to express the geometric mean in simplest radical form.