Find the geometric mean of 500 and 8000.

Geometric mean of two numbers $a$ and $b$ is:

$\sqrt{a \cdot b}$

Step 1: Apply formula

$\sqrt{500 \times 8000}$

Step 2: Multiply

$500 \times 8000 = 4,000,000$

Step 3: Square root

$\sqrt{4,000,000} = 2000$

Final Answer: 2000