Simplify. Assume \( y \) is greater than or equal to zero. \( 9 \sqrt{8 y} \)

To simplify the expression \( 9 \sqrt{8y} \) with the condition that \( y \geq 0 \), follow these steps: 1. **Factor the Radicand:** Start by factoring the number inside the square root to simplify the expression. \[ \sqrt{8y} = \sqrt{4 \times 2y} \] 2. **Simplify the Square Root:** Use the property of square roots that \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \). \[ \sqrt{4 \times 2y} = \sqrt{4} \times \sqrt{2y} = 2 \sqrt{2y} \] 3. **Multiply by the Coefficient:** Now, multiply the simplified square root by the coefficient outside the square root (which is 9). \[ 9 \times 2 \sqrt{2y} = 18 \sqrt{2y} \] **Final Simplified Form:** \[ 18 \sqrt{2y} \]