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 .

Answer

Let's solve the question step by step.

### Step 1: Analyze the first statement
**Statement (i): Every irrational number is a real number.**

- **Justification**: The set of real numbers consists of both rational and irrational numbers. By definition, irrational numbers cannot be expressed as a fraction of two integers, but they still belong to the set of real numbers. Therefore, this statement is true.

### Step 2: Analyze the second statement
**Statement (ii): Every point on the number line is of the form `sqrt(m)`, where m is a natural number.**

- **Justification**: The number line includes all real numbers, which consist of rational numbers (like 1, -3, 0.5) and irrational numbers (like √2, π). Not every point on the number line can be expressed as the square root of a natural number. For example, the number 1.5 cannot be expressed in that form. Therefore, this statement is false.

### Step 3: Analyze the third statement
**Statement (iii): Every real number is an irrational number.**

- **Justification**: Real numbers include both rational numbers (like 1, -2, 0.75) and irrational numbers (like √2, π). Since rational numbers are also part of the real numbers, the statement that every real number is an irrational number is incorrect. Therefore, this statement is false.

### Summary of Answers
1. **Statement (i)**: True
2. **Statement (ii)**: False
3. **Statement (iii)**: False

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