Exercise 1.2 

Q1. 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.  (True)

Justification: Real numbers are collections of both rational and irrational numbers. 

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

Justification: Number line contains both negative and positive integers where m is a natural number, so there is no possibility to express negative number within square root. 

(iii) Every real number is an irrational number.  (False) 

Justification: Real numbers are collections of both rational and irrational numbers not only irrational number. 

Q2. 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.

Solution: No, the square roots of all positive integers are not only irrational but also they are rational. 

Examples: 

​√1 = 1        rational 

√2 = √2      irrational 

√3 = √3      rational 

√4 = 2        rational 

√9 = 3        rational 

Q3. Show how 5 can be represented on the number line.

Solution: