Really none of the above.
A principal square root of a real number is a positive real number (or a positive real number times i, if you're up to complex numbers, but let's assume not.) It's not necessarily a positive integer, √2 being the obvious example.
Is √2 a positive fraction? We can write it as √2 / 1 so I suppose it is. It's certainly not a rational number. Even if we grant irrationals as fractions surely √0=0 isn't a positive fraction. So "always" isn't correct.
I'd go with none of the above, but if I had to choose I'd choose D.