The Kato Square Root Problem follows from an extrapolation property of the Laplacian

On a domain Ω ⊆  _ R^d we consider second-order elliptic systems in divergence-form with bounded complex coefficients, realized via a sesquilinear form with domain H^{1/0 (}Ω) ⊆ V ⊆ H¹ (Ω). Under very mild assumptions on  Ω and V we show that the solution to the Kato Square Root Problem for such systems can be deduced from a regularity result for the fractional powers of the negative Laplacian in the same geometric setting. This extends earlier results of McIntosh [25] and Axelsson-Keith-McIntosh [6] to non-smooth coefficients and domains.