Simplify the following expression. \( \sqrt{5} \cdot \sqrt{50} \)

To simplify the expression \( \sqrt{5} \cdot \sqrt{50} \), follow these steps: 1. **Use the Product Property of Square Roots:** The product of two square roots can be combined under a single square root: \[ \sqrt{5} \cdot \sqrt{50} = \sqrt{5 \times 50} = \sqrt{250} \] 2. **Simplify \( \sqrt{250} \):** Factor 250 into its prime factors to identify perfect squares: \[ 250 = 25 \times 10 = 5^2 \times 10 \] Now, apply the square root to each factor: \[ \sqrt{250} = \sqrt{5^2 \times 10} = \sqrt{5^2} \times \sqrt{10} = 5\sqrt{10} \] So, the simplified form of \( \sqrt{5} \cdot \sqrt{50} \) is: \[ 5\sqrt{10} \] **Answer:** \(5\sqrt{10}\)