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 √m, where m is a natural number.
iii) Every real number is an irrational number.

Solution:

i) Every irrational number is a real number.

This statement is true because the set of real numbers, rational numbers and irrational numbers. For example, √2 is an irrational number which is also a real number. Thus, irrational numbers are a subset of real numbers.

ii) Every point on the number line is of the form √m, where m is a natural number.

This statement is false. For example, the number √2 / 3 is a real number on the number line but 2/3 is not a natural number. (Note that 2/3 is a rational number).

iii) Every real number is an irrational number.

This statement is false. Note that the set of real numbers consists of both rational numbers and irrational numbers. For example, 1/2 is a rational number and hence it is a real number. But it is not an irrational number.

☛ Check: CBSE Class 9 Maths Chapter 1 NCERT Solutions

Video Solution:

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 √m, where m is a natural number. iii) Every real number is an irrational number.

NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.2 Question 1:

Summary:

The statement "Every irrational number is a real number" is true, and the statements "Every point on the number line of the form √m, where 'm' is a natural number" and "Every real number is an irrational number" are false.

☛ Related Questions:

• Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.
• Show how √5 can be represented on the number line.