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.

Learn how to simplify and calculate the expression 3√512 with step-by-step instructions. This math problem involves simplifying square roots and applying the laws of exponents. Suitable for students in Grades 9-10.

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