Simplify. Assume \( x \) is greater than or equal to zero. \( \sqrt{20 x^{3}} \)

To simplify the expression \(\sqrt{20x^{3}}\) with the assumption that \(x \geq 0\), follow these steps: 1. **Factor the Radicand:** \[ 20x^{3} = 4 \times 5 \times x^{2} \times x \] Here, \(4\) and \(x^{2}\) are perfect squares. 2. **Apply the Square Root to Each Factor:** \[ \sqrt{20x^{3}} = \sqrt{4 \times 5 \times x^{2} \times x} = \sqrt{4} \times \sqrt{5} \times \sqrt{x^{2}} \times \sqrt{x} \] 3. **Simplify Each Square Root:** \[ \sqrt{4} = 2,\quad \sqrt{x^{2}} = x \quad (\text{since } x \geq 0) \] So, \[ \sqrt{20x^{3}} = 2 \times x \times \sqrt{5x} = 2x\sqrt{5x} \] **Final Simplified Form:** \[ 2x\sqrt{5x} \]