# Will irrational parameters make a problem not well-defined on complexity

Given a set $$𝑁=\{𝑎_1,⋯,𝑎_𝑛\}$$ where all $$𝑎_𝑖$$s are rational positive numbers and $$\sum_{i\in N}a_i=1$$, find a subset 𝑆⊆𝑁 such that $$(\sqrt{2\sum_{i\in S}a_i}-1)^2$$ is minimized. Does the appearance of √ make the problem ill-defined with regrading to complexity? If well-defined, it is NP-hard, right?