Answer:[tex]16 \sqrt{2} [/tex]Step-by-step explanation:Step 1: The geometric mean of two numbers is the square root of their product.Step 2: In this case the geometric mean is [tex] \sqrt{1 \times 512} = \sqrt{512} [/tex]Step 3: Simplify [tex] \sqrt{512} = \sqrt{ {2}^{9} } = {2}^{ \frac{9}{2} } = {2}^{4} \times \sqrt{2} = 16 \sqrt{2} [/tex]