Curve fitting square of function

I have some data points s_j for i=1...12 and a fitting function with 4
free parameters. The function is of the form f = sqrt(g(x_i,t)) with i
= 1,2,3,4. I was wondering if there's any merit in fitting the square
of the data points (s_j)^2 to g, instead of s_j to f.

Thus minimizing (f(x)^2-(s_j)^2)^2 instead of (f(x)-s_j)^2.

I understand the noise statistics of the data squared are not the same
as the original data... but the objective is still quadratic, I think,
which is what matters.

.

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