Linear systems: Square root of input product
Let $x_1(t) = t^2$ and $x_2(t) = 1$. We have $$y_1(t) =\sqrt{(t-1)^2(t+1)^2}$$ $$y_2(t) = 1$$
Now let $x_3(t) = x_1(t) + x_2(t) = t^2 + 1$. Then we have $$y_3(t) = \sqrt{((t-1)^2 +1)((t+1)^2 +1)}$$ Obviously $$y_3(t) \not = y_1(t) + y_2(t)=\sqrt{(t-1)^2(t+1)^2} +1$$Therefore the system isn't linear.