The halving could come from an intended use in a Newton Raphson iteration of a square root refinement. See for example https://math.mit.edu/~stevenj/18.335/new

The halving could come from an intended use in a Newton Raphson iteration of a square root refinement. See for example https://math.mit.edu/~stevenj/18.335/newton-sqrt.pdf https://math.mit.edu/~stevenj/18.335/newton-sqrt.pdf The initial guess is the approximate square root, but it needs to be halved as part of the calculation.