Sure; for example, 10 + pi is irrational, 10 - pi is irrational. Both are positive. If you add them, you get 20.
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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.
Next to any rational number is an irrational number, but next to an irrational number can be either a rational number or an irrational number, but it is infinitely more likely to be an irrational number (as between any two rational numbers are an infinity of irrational numbers).
It will be irrational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
Positive rational = 0.0000000001Positive irrational = 0.0000000001*pi
No, no number can be both rational and irrational.