Simplify the radical expression. \[ \sqrt{50} \]

To simplify the radical expression \(\sqrt{50}\), follow these steps: 1. **Factor the Number Inside the Radical:** Break down 50 into its prime factors: \[ 50 = 25 \times 2 \] Here, 25 is a perfect square since \(25 = 5^2\). 2. **Apply the Square Root Property:** The square root of a product is the product of the square roots: \[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} \] 3. **Simplify the Square Root:** Since \(\sqrt{25} = 5\), substitute this value: \[ \sqrt{50} = 5 \times \sqrt{2} = 5\sqrt{2} \] **Final Simplified Form:** \[ \sqrt{50} = 5\sqrt{2} \]