The paper presents the design and implementation of a two-bit optical divider circuit using a new approach based on micro-optical ring resonators. Additionally, the proposed circuit is utilized as a fundamental component in an optical square root evaluator, showcasing the potential of optical computing. The design of the two-bit optical divider circuit leverages the unique properties of micro-optical ring resonators (MORR) to achieve efficient two-bit optical division. By exploiting the phenomenon of light interference within the MORR having a small radius(R = 3.546um), precise optical division of the input binary numbers is accomplished with a minimal power of 1.19 mW. Furthermore, the paper explores the integration of the designed two-bit optical divider circuit into a square root evaluator. Through rigorous simulation of the developed Transfer function in the Z-domain, the performance of the two-bit optical divider and the square root evaluator using the proposed two-bit divider circuit is evaluated and validated by some essential parameters such as extinction ratio, contrast ratio, and Amplitude Modulation demonstrate the significant advantages underscoring its potential for transformative computing applications.