1. The problem is to find the cube root of 343. 2. The cube root of a number $x$ is a number $y$ such that $y^3 = x$. 3. We want to find $y$ such that $$y^3 = 343$$ 4. Recognize that $343 = 7^3$ because $7 \times 7 \times 7 = 343$. 5. Therefore, $$\sqrt[3]{343} = 7$$ 6. The cube root of 343 is 7.