The diagonal of a unit square, for example, is radical(2).
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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.
A fjord is a real world example of a fjord! They exist in the real world.
y = cuberoot(x) for real x is not a rational function.
It can be.
y=x2