1. **State the problem:** Solve the equation $$27 = x^3$$ for real number $$x$$. 2. **Formula and rules:** To solve for $$x$$ when given $$x^3 = a$$, use the cube root formula: $$x = \sqrt[3]{a}$$ The cube root of a number $$a$$ is the number that, when cubed, gives $$a$$. 3. **Apply the formula:** $$x = \sqrt[3]{27}$$ 4. **Evaluate the cube root:** Since $$27 = 3^3$$, we have $$x = 3$$ 5. **Check for other solutions:** For real numbers, the cube root function has exactly one real root. So the only real solution is $$x = 3$$. **Final answer:** $$x = 3$$