1. **State the problem:** Find the cube root of 27, which is written as $\sqrt[3]{27}$. 2. **Recall the definition:** The cube root of a number $a$ is a number $b$ such that $b^3 = a$. 3. **Apply the definition:** We want to find $b$ such that $b^3 = 27$. 4. **Evaluate:** Since $3^3 = 3 \times 3 \times 3 = 27$, it follows that $\sqrt[3]{27} = 3$. 5. **Final answer:** $$\sqrt[3]{27} = 3$$