Question: Solve the equation using inverse operations: \n\n$\sqrt{x} = 11$
1. **State the problem:** We need to solve the equation $$\sqrt{x} = 11$$ for $x$.\n\n2. **Recall the formula and rule:** The square root function $\sqrt{x}$ is the inverse of squaring. To undo the square root, we square both sides of the equation.\n\n3. **Apply inverse operation:** Square both sides to eliminate the square root:\n$$\left(\sqrt{x}\right)^2 = 11^2$$\n\n4. **Simplify:**\n$$x = 121$$\n\n5. **Check the solution:** Substitute $x=121$ back into the original equation:\n$$\sqrt{121} = 11$$ which is true.\n\n**Final answer:** $$x = 121$$