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

## Question

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

## 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.