Real numbers are those which can be placed upon a number line stretching to infinity in both directions. To be "not real" you must be unable to do that. We call "not real" numbers "imaginary" numbers. They are numbers which are derived from the square root of -1. If you think about it, what number can be multiplied by itself and you end up with -1. In the real numbers, there isn't one. So we have imaginary numbers. They are written using Euler's notation where i represents the square root of -1. So, to answer your question, i is a "not real" number.
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2 is a real number.
The square root of 2 is real number but it is not rational number because it can't be expressed as a fraction.
Any odd root, for example the cube root, of -3.24 is a real number.
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No, the devil's phone number is not real. Many associate the numbers 666 with the devil.