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Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number
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 , where m is a natural number. (iii) Every real number is an irrational number.
(i) True, since the collection of real numbers comprises of rational and irrational numbers.
(ii) False, because negative numbers cannot be expressed as the square root of any natural number.
(iii) False. Real numbers include both rational and irrational numbers. Hence, every real number cannot be an irrational number.
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