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 $\sqrt{m},$ where $^{'} m^{'}$ is a natural number.
(iii) Every real number is an irrational number.

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Solution

(i) True; since the collection of real numbers is made up of rational and irrational numbers.
(ii) False; as negative numbers cannot be expressed as the square root of any other number.
(iii) False; as real numbers include both rational and irrational numbers. Therefore, every real number cannot be an irrational number.

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State whether the following statements are true or false. Justify your answer.

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