1. **State the problem:** Evaluate the integral $$\int_0^1 8 \, dx$$ and then add $$\sqrt{8}$$ to the result. 2. **Recall the formula for definite integrals:** $$\int_a^b c \, dx = c(b - a)$$ where $$c$$ is a constant. 3. **Apply the formula:** Here, $$c = 8$$, $$a = 0$$, and $$b = 1$$. $$\int_0^1 8 \, dx = 8(1 - 0) = 8$$ 4. **Calculate the square root:** $$\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}$$ 5. **Add the results:** $$8 + 2\sqrt{2}$$ 6. **Final answer:** $$8 + 2\sqrt{2}$$