In a statistics class, the geometric mean of two positive numbers $a$ and $b$ is defined as $\sqrt{a\times b}$. What is the geometric mean of 14 and 20?

• A. $\sqrt{14+20}$ (approximately $5.83$)
• B. $\frac{2}{\frac{1}{14}+\frac{1}{20}}$ (approximately $16.47$)
• C. $\sqrt{280}$ (approximately $16.73$)
• D. $\frac{14+20}{2}$ (which equals $17$)

Answer: (C)

Verified step by step guidance

1. Recall the definition of the geometric mean for two positive numbers \(a\) and \(b\): it is given by the square root of their product, which can be written as \(\sqrt{a \times b}\).
2. Identify the two numbers given in the problem: \(a = 14\) and \(b = 20\).
3. Calculate the product of the two numbers: multiply 14 by 20 to get \(14 \times 20\).
4. Take the square root of the product obtained in the previous step: \(\sqrt{14 \times 20}\).
5. This expression \(\sqrt{280}\) represents the geometric mean of 14 and 20. You can then approximate this value using a calculator if needed.