Statistical solutions for quadratic and square root polynomials of second order for a group of (1/5) (5x5x5) fractional factorials when the design is completely randomized is briefly considered in this text. The extension of the fractional factorial (1/5) (5x5x5) to a type of block design with utilization of the quadratic polynomial model in order to eliminate linear and quadratic effect of gradient or other systematic causes is proposed, its statistical analysis developed and the detailed solution presented. Using proper range of dosages in order to eliminate large areas of plateau response stimulus as happens in nutrient experiments or fertilizer experiments, this design makes feasible efficient estimation of the coefficients that measure the curvature of the response functions on the area of economical decision. So better solution in the determination of the dosage of nutrients to achieve maximum response or the dosages that determine the optimum economical response are achieved with experiments of medium size. This design will fit well those cases in which the use of three factors at several levels each is desirable and where the presence of treatments in which the dosages vary simultaneously for the three factors is important (area of higher probable response in the case of nutrients, for example) and the remaining treatments are uniformly spread inside the cube of the area of stimulus, under investigation. Using the property of the four orthogonal latin-squares as presented by Fisher and Yates, the fractional factorial (1/25) (5x5x5x5) designs were proposed as a completely randomized type; they allow the simultaneous study of four factors at five levels each, with a reduced number of points.