What is the geometric mean of 5 and 20?

• A. $10$
• B. $12.5$
• C. $25$
• D. $15$

Answer: (A)

Verified step by step guidance

1. Recall that the geometric mean of two positive numbers \(a\) and \(b\) is given by the formula: \(\text{Geometric Mean} = \sqrt{a \times b}\).
2. Identify the two numbers given in the problem: \(a = 5\) and \(b = 20\).
3. Substitute these values into the formula: \(\sqrt{5 \times 20}\).
4. Calculate the product inside the square root: \$5 \times 20 = 100$.
5. Take the square root of 100 to find the geometric mean: \(\sqrt{100}\).