Well, isn't that a happy little question! No, 2.236068 is not a rational number. It is actually an irrational number because it cannot be expressed as a simple fraction of two integers. Just like every tree and cloud in nature, numbers come in all different shapes and sizes, and that's what makes them so special.
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Yes.
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It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
Yes. Any rational number divided by another rational number is also rational.