Question

are irrational numbers real numbers?

Answer 1

Yes, irrational numbers are a subset of real numbers. Real numbers include all the rational numbers (which can be expressed as fractions) and all the irrational numbers (which cannot be expressed as fractions). Examples of irrational numbers include √2, π, and e. They cannot be written as a ratio of two integers, whereas rational numbers can. So, in summary, all irrational numbers are indeed real numbers.