How to deal with loss of significance in the case $f(x) = \sqrt{x+2} -\sqrt{x}$?

I would like to evaluate the expression $ f(x) = \sqrt{x+2} -\sqrt{x}$ with cases when $ x = 3.2 \times 10^{30}$ and $ x= 3.2 \times 10^{16}$ . I tried using N[Sqrt[x+2] - Sqrt[x], 100] and

ScientificForm[Sqrt[x+2] - Sqrt[x], 100], both yielding 0 as an output. How can I obtain the desired output?

I also tried the method in Making a calculation with high precision by applying .`100 as a suffix but my mathematica 12 doesn’t seem to be recognizing it.