A real number that can not be expressed as a rational number.
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No. Irrational numbers by definition fall into the category of Real Numbers.
Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
Yes, irrational numbers are never rational numbers because irrational numbers can't be expressed, by definition, as a fraction of two integers.
Yes. The definition of a surd is "an irrational number"
It is a non-terminating, non-repeating decimal representation. That is a definition of irrational numbers.