The answer depends on what group or field the function is defined on.
In the complex plane, the range is the complex plane.
If the domain is all real numbers and the radical is an odd root (cube root, fifth root etc), the range is the real numbers. Otherwise, it is the complex plane.
If the domain is non-negative real numbers, the range is also the real numbers.
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You need to know the domain in order to find the range.
A function that has a variable under a radical sign.
The domain is a subset of the values for which the function is defined. The range is the set of values that the function takes as the argument of the function takes all the values in the domain.
The diagonal of a unit square, for example, is radical(2).
Find the maximum and minimum values that the function can take over all the values in the domain for the input. The range is the maximum minus the minimum.