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.
$(i)$ 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.
(N/A) $(i)$ True; the set of real numbers consists of both rational and irrational numbers. Therefore,every irrational number is a real number.
$(ii)$ False; negative numbers on the number line cannot be expressed as the square root of any natural number $m$,as the square root of any natural number is always non-negative.
$(iii)$ False; real numbers include both rational and irrational numbers. For example,$2$ is a real number but it is a rational number,not an irrational number.
$(ii)$ False; negative numbers on the number line cannot be expressed as the square root of any natural number $m$,as the square root of any natural number is always non-negative.
$(iii)$ False; real numbers include both rational and irrational numbers. For example,$2$ is a real number but it is a rational number,not an irrational number.
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