1. The problem is to find the cube root of 49, written as $\sqrt[3]{49}$. 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 $y^3 = 49$. 4. Since 49 is not a perfect cube, we can approximate the cube root using prime factorization or a calculator. 5. Prime factorization of 49 is $7^2$, and since the exponent 2 is less than 3, it cannot be simplified further as a cube root. 6. Therefore, $\sqrt[3]{49}$ remains as is or can be approximated numerically. 7. Using a calculator, $\sqrt[3]{49} \approx 3.659$. Final answer: $$\sqrt[3]{49} \approx 3.659$$