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Possibly 5th Century BC
Probably the ancient Egyptians who discovered that the diagonal of a unit square was not a rational number. And then discovered other such numbers.
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.
He got killed
Pythagoras discovred it to find unknown sides in a right angled triangle