Ex.1.2 Q1 Number System Solution - NCERT Maths Class 9

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

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Number Systems
Ex 1.2 | Question 1

Text Solution

(i) Every irrational number is a real number.


True, because the set of real numbers consists of rational numbers and irrational numbers.

(ii) Every point on the number line in of the form \(\begin{align}\,\sqrt m ,\end{align}\) where \(m\) is a natural number.


False, for example \(\begin{align}\sqrt {\frac{2}{3}} \end{align}\) is a real number on the number line but \(\begin{align}\frac{2}{3}\end{align}\) is not a natural number (Note that \(\begin{align}\frac{2}{3}\end{align}\) is a rational number).

(iii) Every real number is an irrational number.


False. Note that the set of real numbers contains both rational and irrational numbers. As an example, \(\begin{align}\frac{1}{2}\end{align}\) is a rational number and hence it is real. But it is not an irrational number.

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