Consider an elliptic sesquilinear form defined on × by , where is a closed subspace of H¹(Ω) which contains C₀^∞(Ω), Ω is a bounded Lipschitz domain in ⁿ, a_jk, a_k, α_j, a ε L_∞(Ω), and Re a_jkζ_kζ_j κ > 0 for all ζεⁿ with ¦ζ¦ = 1. Let L be the operator with largest domain satisfying J[u, v] = (Lu, v) for all υ. Then L + λI is a maximal accretive operator in L₂(Ω) for λ a sufficiently large real number. It is proved that (L + λI)^1/2 is a bounded operator from to L₂(Ω) provided mild regularity of the coefficients is assumed. In addition it is shown that if the coefficients depend differentiably on a parameter t in an appropriate sense, then the corresponding square root operators also depend differentiably on t. The latter result is new even when the forms J are hermitian.