To solve $\sqrt[3]{512}$, we are looking for the cube root of 512. This means finding a number that, when multiplied by itself three times, equals 512.

Solution:

$512 = 8 \times 8 \times 8 = 8^3$ Therefore, $\sqrt[3]{512} = 8$

The answer is 8.

Would you like further details on cube roots or have any other questions?

Here are some related questions:

1. What is the cube root of 729?
2. How do you find the cube root of a number without a calculator?
3. Can negative numbers have real cube roots?
4. What is the fourth root of 256?
5. How does finding the cube root differ from finding the square root?

Tip: Remember, cube roots of perfect cubes (like 512, 729, etc.) are integers, which can help in quick mental calculations.