Yes it is, but not every real number is a rational number
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False.
No. Though every perfect square is a rational number, not every rational number is a perfect square. Example: 2 is a rational number but sqrt(2) is not rational, so 2 is not a perfect square.
Every rational number does.
Every rational number does.
There is no such thing as a number that is both rational and irrational. By definition, every number is either rational or irrational.