State whether the following statements are true or false. Justify your answers. (i) Every irrational number is a real number. (ii) Every point on the number line is of the form √m, where m is a natural number. (iii) Every real number is an irrational number.

(i) True: Real numbers are any number which we can think of. Thus, every irrational number is a real number. (ii) False: A number line may have negative or positive numbers. Since no negative number can be the square root of a natural number, thus every point on the number line cannot be in the form of √m, where m is a natural number. (iii) False: All numbers are real numbers, and non-terminating, non-repeating numbers are irrational numbers. For example, 2, 3, 4, etc. are some examples of real numbers and these are not irrational.