1. **State the problem:** Solve the equation $$\sqrt{x} + 2 = 8$$ and check the solution. 2. **Isolate the square root term:** Subtract 2 from both sides: $$\sqrt{x} + 2 = 8 \implies \sqrt{x} = 8 - 2$$ $$\sqrt{x} = 6$$ 3. **Square both sides to eliminate the square root:** $$\left(\sqrt{x}\right)^2 = 6^2$$ $$x = 36$$ 4. **Check the solution:** Substitute $x=36$ back into the original equation: $$\sqrt{36} + 2 = 6 + 2 = 8$$ The left side equals the right side, so $x=36$ is a valid solution. **Final answer:** $$x = 36$$