**Find the real solution(s) of the following equation.**

\[x^3 = 512\]

The given equation is:

\[
x^3 = 512
\]

To solve for \(x\), we take the cube root of both sides:

\[
x = \sqrt[3]{512}
\]

Since \(512 = 8^3\), the cube root of \(512\) is 8:

\[
x = 8
\]

Thus, the real solution is:

\[
x = 8
\]

Would you like a detailed explanation of how cube roots work?

Here are 5 related questions for you to consider:
1. How would you solve \(x^3 = -512\)?
2. What is the cube root of \(1000\)?
3. What are the real solutions to \(x^3 = 27\)?
4. How would you solve \(x^4 = 16\)?
5. Can a cubic equation have more than one real solution?

**Tip**: When solving equations involving cubes, remember that cube roots of positive numbers are positive, while cube roots of negative numbers are negative.

Find the real solution(s) of the following equation.
x^3 = 512

Explore the step-by-step solution to the cubic equation x^3 = 512. Learn about cube roots, how to apply them, and how to find the real solution x = 8. This problem covers essential algebraic concepts, suitable for students in Grades 8-10.

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