Floating-point square-root computation is a power- and delay-critical operation in edge-AI, signal-processing, and embedded systems. Conventional implementations typically rely on multipliers or iterative pipelines, resulting in increased hardware complexity, switching activity, and energy consumption. This work presents E2AFS, a lightweight and fully multiplier-free floating-point square-root architecture optimized for energy-efficient computation. By reducing logic depth and minimizing switching activity, the proposed design achieves substantial improvements in hardware efficiency and performance. FPGA implementation on an Artix-7 device demonstrates that E2AFS achieves the lowest dynamic power (7.63 mW), the shortest critical-path delay (4.639 ns), and the minimum power-delay product (35.39 pJ) compared to existing ESAS and CWAHA architectures. Error evaluation using multiple accuracy metrics, together with graphical analysis, shows that E2AFS closely approximates the exact square-root function with consistently low deviation. Application-level validation in Sobel edge detection and K-means color quantization further confirms its suitability for low-power real-time edge and embedded platforms.

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