To calculate $3 \sqrt{512}$:

1. Start by simplifying $\sqrt{512}$.

   $\sqrt{512} = \sqrt{2^9} = 2^{\frac{9}{2}} = 2^4 \cdot \sqrt{2} = 16 \sqrt{2}$

2. Now multiply the result by 3:

   $3 \cdot 16 \sqrt{2} = 48 \sqrt{2}$

So, the final answer is:

$\boxed{48 \sqrt{2}}$

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

1. How do you simplify square roots of other powers of 2, such as $\sqrt{256}$?
2. What is the value of $\sqrt{2}$ approximately?
3. How do you multiply numbers by square roots?
4. Can you simplify $4 \sqrt{200}$ similarly?
5. What is the process for simplifying cube roots like $\sqrt[3]{512}$?

Tip: When simplifying square roots, look for perfect squares within the radicand to simplify your calculations easily.