The QR-decomposition (QRD)-based recursive least-squares (RLS) methods have been shown to be useful and effective towards adaptive signal processing in modern communications, radar, and sonar systems implementable with various modern parallel and systolic array architectures. The planar (Givens) and hyperbolic rotations are the most commonly used methods in performing the QRD up/downdating. But the generic formula for these rotations require explicit square-root (sqrt) computations, which constitute the computational bottleneck and are quite undesirable from the practical VLSI circuit design point of view. There has been more than ten sqrt-free algorithms known so far. In this paper, we provide a unified systematic approach for the sqrt-free QRD-based RLS estimation problem. By properly choosing two parameters, and v, all existing known sqrt-free methods fall in the category of our unified approach. The proposed method not only can generalize all currently known sqrt-free QRD algorithms, but also new sqrt-free algorithms as long as the parameters and v are properly chosen. The unified treatment is also extended to the QRD-based RLS problems for optimal residual acquisition without sqrt operations, and the systolic array implementation.