What is the geometric mean of $4$ and $9$?

• A. $13$
• B. $6.5$
• C. $6$
• D. $5$

Answer: (C)

Verified step by step guidance

1. Identify the numbers for which you want to find the geometric mean. In this case, the numbers are 4 and 9.
2. Recall the formula for the geometric mean of two numbers \(a\) and \(b\): \[\\text{Geometric Mean} = \\sqrt{a \\times b}\]
3. Substitute the given numbers into the formula: \[\\text{Geometric Mean} = \\sqrt{4 \\times 9}\]
4. Calculate the product inside the square root: \[4 \\times 9 = 36\]
5. Take the square root of the product to find the geometric mean: \[\\sqrt{36}\]