1. **Problem Statement:** We need to simplify and evaluate the expression $\sqrt{1^3 + 2^3}$. 2. **Recall the formula and rules:** - The cube of a number $a$ is $a^3 = a \times a \times a$. - The square root $\sqrt{x}$ is the number which when squared gives $x$. - We will first calculate the cubes, then add, and finally take the square root. 3. **Calculate the cubes:** - $1^3 = 1 \times 1 \times 1 = 1$ - $2^3 = 2 \times 2 \times 2 = 8$ 4. **Add the cubes:** - $1 + 8 = 9$ 5. **Take the square root:** - $\sqrt{9} = 3$ 6. **Final answer:** - The value of $\sqrt{1^3 + 2^3}$ is $3$. This means the expression simplifies neatly to 3.