Question

does real numbers contains irrational numbers

Answer 1

Yes real number contains √ 2

Answer 2

The real numbers include all therational numbers, such as the integer −5 and the fraction 4/3, and all theirrational numbers, such as √2 (1.41421356..., the square root of 2, anirrational algebraic number). Included within the irrationals are the transcendental numbers, such as π (3.14159265...).