1. **State the problem:** Simplify the expression $\sqrt{50}$. 2. **Recall the formula and rules:** The square root of a product can be expressed as the product of the square roots: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$ 3. **Factorize 50:** $$50 = 25 \times 2$$ 4. **Apply the square root to each factor:** $$\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2}$$ 5. **Evaluate the square root of 25:** $$\sqrt{25} = 5$$ 6. **Combine the results:** $$\sqrt{50} = 5 \times \sqrt{2} = 5\sqrt{2}$$ **Final answer:** $$\boxed{5\sqrt{2}}$$