Usually four. As a simple example, the fourth roots of 1 are: 1, -1, i, -i.
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The answer will depend on the form of the fourth root. Positive real numbers will have two fourth roots which are real and two that are complex. Complex numbers will have four complex roots. However, none of these can be "simplified" in the normal sense of the term.
Two of the four roots are 1.8212 and -1.8212 (approx). The other two roots are complex numbers.
There are 3 cube roots of 27. There are 2 square roots of 27 ( or any real number ). There are 4 fourth roots of 27 and so on:)
In general, the answer is 4, but only 2 of them are real. For example, the 4th roots of 16 are 2, -2, 2i, and -2i.
They are numbers that are formed by linear combinations of square roots, cube roots (and other higher roots) of numbers which cannot be simplified into ratios of integers (ie rational numbers). The linear combinations may also contain integers. A linear combination is simply a way of saying so many sqrt(2)s plus that many cuberoot(7)s etc.