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This is best done if the complex number is in polar coordinates - that is, a distance from the origin, and an angle. Take the square root of the argument (the absolute value) of the complex number; and half the angle.
The fourth square root is the 16th root of a number. On a computer, to find the 16th root of a number, say 5.6, enter 5.6^(1/16). If the number you start with is positive, you will have 2 real roots (one positive and one negative) and 14 complex roots. If it is negative, you will have 16 complex roots.
You can take the square root of a negative number by using complex numbers and the "i" operator. (-300)^.5 = (-1 * 300)^.5 = (-1)^.5 * 300^.5 = i17.32 because i = (-1)^.5
Precisely because of what you are saying, the square root of -36 is not -6. The square root is defined, precisely, as the number which, when squared, gives you back the original number, in this case -36; and that isn't the case if you assume that -6 is the square root.The square root of a negative number can not be taken if you only accept real numbers as solutions. If you accept complex numbers as solutions - and rest assured that complex numbers do have applications in many areas - then you can take the square root of any real (or complex) number. In this case, the square root of -36 is 6i, where "i" is the so-called "imaginary unit".
Measure it. Or take a quarter of its perimeter. Or take the square root of its area. Or take the cube root of a cube built on the square