1. The problem is to find the cube root of 64, written as $\sqrt[3]{64}$. 2. The cube root of a number $x$ is a value $a$ such that $a^3 = x$. 3. We want to find $a$ such that $a^3 = 64$. 4. Since $64 = 4^3$, it follows that $\sqrt[3]{64} = 4$. 5. Therefore, the cube root of 64 is 4.