Q: Is an irrational number cannot be a real number?

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No it cannot. Irrational means "not rational".

Any real number which cannot be expressed as a ratio of two integers is an irrational number.

Pi. That is an irrational number. Irrational numbers cannot be expressed as a fraction.

An irrational number is a real number that cannot be expressed as a ratio of two integers.

A rational number cannot also be irrational. A real number is either rational, or it is irrational.

False.

An irrational number is a real number that is not ration. That is, it is a real number than cannot be expressed as a ratio of two integers: that is, as a/b where b is not zero.

No. Real numbers are divided into two DISJOINT (non-overlapping) sets: rational numbers and irrational numbers. A rational number cannot be irrational, and an irrational number cannot be rational.

An irrational number is a real number that is not rational. A rational number is one that can be expressed as a ratio of two integers. An irrational number cannot be expressed in this way.

An irrational number.

When it is a real number that cannot be expressed as a ratio of two integers.

An irrational number is any real number that cannot be expressed as a ratio of two integers.So yes, an irrational number IS a real number.There is also a set of numbers called transcendental numbers, which includes both real and complex/imaginary numbers. Of this set, all the real numbers are irrational numbers.