Looking at the graphs of function growth, I noticed the growth for square root function is similar to the growth of a logarithmic function and thought they are the same but turns out logarithmic function grows much slower than the square root function and that square root function grows much slower than the linear function.

In short, the function growth of square root function is bounded on top by the linear function's and bounded below by the logarithmic function. Logarithmic function still grows the slowest.