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Summary: The geometric mean is typically used to measure the mean of inflation rate and population fluctuation. It is also used in the description and analysis of singularities and geometric distance spaces. Gradient descent is an integral part of artificial intelligence. In this study, we transform the gradient calculation from conventional quadratic gradient descent algorithms into a root extraction calculation using geometric means. To eliminate the computational complexity of differential operations in gradient calculation and to easily calculate roots using only fundamental arithmetic operations, we introduce the Kai Fang method, the East Asian traditional root extraction method. To do this, we propose a new quadratic gradient descent method based on geometric means and we apply the Kai Fang method with geometric means to create an improved quadratic gradient descent method. The proposed method shows improved computational ease over conventional methods. [ABSTRACT FROM AUTHOR]