It certainly can! All Irrational Numbers (numbers that can't be written as fractions, and in decimal form go endlessly without a pattern) are real (not divided by zero and not connected to the square root of a negative number).
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No. All irrational numbers are real, not all real numbers are irrational.
Every irrational number is a real number.
An irrational number is a real number.
A real number which is not a rational number is an irrational number.
All real numbers are irrational. For example, Pi is an irrational number that is a real number. Other irrational numbers can be the square root of an imperfect square.