Yes.
pi - sqrt(2) is irrational.
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Not necessarily. The sum of two irrational numbers can be rational or irrational.
Yes. Example: pi - pi = 0.You can even subtract two different irrational numbers to get a rational number.For example: e - (e - 1) = 1 or Φ - (1/Φ) = 1.
yes * * * * * No. Rational and irrational numbers are two DISJOINT subsets of the real numbers. That is, no rational number is irrational and no irrational is rational.
you can't FIGURE OUT THE SQUARE OF THE IRRATIONAL NUMBER
Yes, you can.