-Ushma Gaur, Subject Matter Expert at Edumarz
(i) Every irrational number is a real number.
Solution: True, because the collection of all rational numbers and all irrational numbers together form the collection of real numbers.
(ii) Every point on the number line is of the form √𝒎 where 𝒎 is a natural number.
Solution: False, because negative numbers cannot be the square roots of the natural number. For example, −3 is a real number but it is not the square root of any natural number.
(iii) Every real number is an irrational number.
Solution: False, since irrational numbers are those which cannot be written in the pq form, where 𝑝 and 𝑞 are integers and 𝑞 ≠ 0. For example, 2 is a real number and can be written in the p/q form, i.e. 2/1 but it is not an irrational number.