Every irrational number is a real number.
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No. All irrational numbers are real, not all real numbers are irrational.
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.
No, because it could be a rational number.
The square root of any positive, non-square number will be both real and irrational.
Yes, every irrational number is also a real number. Real numbers include all the numbers on the number line, which consists of both rational and irrational numbers. Rational numbers can be expressed as fractions, whereas irrational numbers cannot be expressed as simple fractions. So, while all irrational numbers are real numbers, not all real numbers are irrational—some are rational.