Find the product of the square root of $256$ and the square root of $16$, and then find the result's square root.

Follow the instructions step-by-step:
1. Find the square root of $256$:

$$\sqrt{256}=16$$

2. Find the square root of $16$:

$$\sqrt{16}=4$$

3. Find the product of these two results:

$$\text{Product}=16\times 4=64$$

4. Find the square root of the final result:

$$\text{Final Result}=\sqrt{64}=8$$