Simplify. Assume \( f \) is greater than or equal to zero. \( \sqrt{18 f^{8}} \)

To simplify the expression \(\sqrt{18 f^{8}}\) with the condition that \(f \geq 0\), follow these steps: 1. **Factor the Radicand:** \[ \sqrt{18 f^{8}} = \sqrt{9 \times 2 \times f^{8}} \] 2. **Simplify the Square Root:** - \(\sqrt{9} = 3\) - \(\sqrt{f^{8}} = f^{4}\) (since \(f \geq 0\)) - \(\sqrt{2}\) remains as it is because 2 is not a perfect square. 3. **Combine the Simplified Parts:** \[ \sqrt{18 f^{8}} = 3 f^{4} \sqrt{2} \] **Final Simplified Form:** \[ 3 f^{4} \sqrt{2} \]