1. **State the problem:** We need to simplify the expression $\sqrt{242}$. 2. **Recall the formula and rules:** The square root of a product can be written as the product of the square roots: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$ 3. **Factorize 242:** $$242 = 121 \times 2$$ 4. **Apply the square root to the factors:** $$\sqrt{242} = \sqrt{121 \times 2} = \sqrt{121} \times \sqrt{2}$$ 5. **Simplify the square root of 121:** $$\sqrt{121} = 11$$ 6. **Write the simplified form:** $$\sqrt{242} = 11 \times \sqrt{2} = 11\sqrt{2}$$ **Final answer:** $\boxed{11\sqrt{2}}$