What is the geometric mean of 8 and 28?

• A. $\frac{8+28}{2}$
• B. $\sqrt{36}$
• C. $\sqrt{224}$
• D. $18$

Answer: (C)

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 the formula: \(\text{Geometric Mean} = \sqrt{a \times b}\).
2. Identify the two numbers given in the problem, which are 8 and 28.
3. Calculate the product of these two numbers: \$8 \times 28$.
4. Take the square root of the product obtained in the previous step: \(\sqrt{8 \times 28}\).
5. Express the result as the geometric mean of 8 and 28, which is \(\sqrt{224}\).