What is the geometric mean of 7 and 12?

• A. $7+12$
• B. $12-7$
• C. $\sqrt{84}$
• D. $\frac{7+12}{2}$

Answer: (C)

Verified step by step guidance

1. Understand that the geometric mean of two numbers is the square root of their product. It is a measure that indicates the central tendency by multiplying the numbers and then taking the root corresponding to the count of numbers.
2. Identify the two numbers given: 7 and 12.
3. Calculate the product of the two numbers: multiply 7 by 12, which gives \$7 \times 12$.
4. Take the square root of the product obtained in the previous step, which is \(\sqrt{7 \times 12}\).
5. Express the geometric mean as \(\sqrt{84}\), since 7 times 12 equals 84.