1. The problem asks to find the exact value of $\cos LL$ in simplest radical form. 2. Since the problem does not specify what $LL$ represents, we need to clarify or assume it refers to a specific angle or length in a geometric figure. 3. Without additional information, we cannot determine the exact value of $\cos LL$. 4. Please provide more details or context about $LL$ (e.g., angle measure, triangle, or figure) to proceed with the calculation.