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