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

Question

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

Video Solution
Number Systems
Ex 1.2 | Question 1

Text Solution

(i) Every irrational number is a real number.

Steps:

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.

Steps:

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.

Steps:

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.

Video Solution
Number Systems
Ex 1.2 | Question 1
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