The given quadratic function is
\[ f(x) = 12(x - 11)^2 + 4. \]
To find the minimum point of this function, we can analyze its structure. This is a parabola that opens upwards (since the coefficient of the squared term is positive, \(12\)). The vertex of a parabola in the form \(f(x) = a(x - h)^2 + k\) is at the point \((h, k)\).
In your function, \(h = 11\) and \(k = 4\). Therefore, the coordinates of the minimum point (the vertex) are
\[ (11, 4). \]
Now, if you are asking about the square root function that relates to \(f(x)\), this function, since it is a quadratic function, has a minimum point at \((11, 4)\) and does not require any additional transformation via a square root function.
Thus, the minimum point for the function \(f(x)\) you provided is
\[ \boxed{(11, 4)}. \]