This paper considers the use of the arithmetic operation of square-rooting in signal processing. Many algorithms have been reformulated to avoid the square root operation in an attempt to increase processing speed. Rather than reformulating the algorithms to be square root free with the inherent problems of numerical instability, loss of orthogonality, and overflow/underflow, the square root is reconsidered from first principles and arrays are designed that are approximately twice as fast and approximately half the chip area of the analagous division. A non-restoring division array is also presented, and it is shown that with minimal modification the array also performs square roots. The result that square rooting is in fact a simpler operation than division has considerable implica-tions for many signal processing algorithms. Two examples are considered; first it is shown that there are no advantages in using square root free Givens transformations in QR triangular arrays; and also contrary to common conception that unnormalised least square lattices are more complex to implement than the square root normalised least squares lattices.