Well, honey, "goggle" may refer to a popular search engine or a pair of swimming goggles, but in the world of mathematics, it ain't no real number. Real numbers are the ones you can count on your fingers and toes, not some fancy word play. So, to answer your question, no, "goggle" is not a real number in the mathematical sense.
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The number is called gogool. It means to to the power 100. You can also have gogool plexes there isn't enough paper and ink in the world to right these numbers out in full let alone the fact you'd be dead before you finnished:)
The square of a real number is always a real number.
Yes, zero is a real number. It is not a counting number, but it is an integer, a rational number, and a real number.
Of course, not only can it be a real number but it is a real number. When you take the square root times itself, the result is a number that is real.
A real number dosen't have to be a rational number as a real number can be rational or irrational i.e the root of 2 is irrational and real. So is (pi).
Any decimal number is a real number.