Page 1.35

### Exercise 1.2

Type 1

#### Question 1

**Are the square roots of all positive integers irrational ? If not, then give an example of the square root of a positive integer which is a rational number.**

Sol :

No; Example: √9=3, which is a rational number

#### Question 2

**Identify two Statements in the following statements :**

**(i) √5 is a rational number**

Sol : False

**(ii) is a rational number**

Sol : False

= rational number

**(iii) Every number which is not an integer, is an irrational number.**

Sol : False, is not an integer but it is not an irrational number.

Type 2

#### Question 3

**Fill in the blanks :**

**(i) Decimal representation of a rational number is __**

Sol :

**(ii) Decimal representation of a rational number is either __ or __**

Sol : Terminating, Recurring

**(iii) Decimal representation of an irrational number is neither __ nor __**

Sol : Terminating, Recurring

**(iv) Corresponding to every point on the number line , there is a __ which is either __ or __**

Sol : Real number, Rational, Irrational

**(v) 0 is a/an __ number. (rational number)**

Sol : Rational

#### Question 4

**Find, which of the variables x,y,z represent rational numbers and which represent irrational numbers ?**

**(i) x ^{2}=15**

Sol: x represents an irrational number

**(ii) y ^{2}=16**

Sol: y represents a rational number

**(iii) z ^{2}=0.09**

Sol: z represents a rational number

#### Question 5

**State, which of the following numbers are rational numbers and which are irrational numbers ?**

**(i) **

Sol : Irrational

**(ii) **

Sol : Irrational

**(iii) **

Sol : Rational

**(iv) 1.232332333…**

Sol : Irrational

**(v) 0.98107**

Sol : Rational

**(vi) 2.201220012220001…**

Sol : Irrational

#### Question 6

**Which of the following number is irrational ?**

**(i) **

Sol:

**(ii) √3**

Sol:

**(iii) **

Sol:

**(iv) **

Sol:

#### Question 7

**Which of the following number is not irrational ?**

**(i) **

Sol:

**(ii) **

Sol:

#### Question 8

**State, which of the following does not belong to the same class :**

**(i) **

Sol :

**(ii) **

Sol :

Category A

#### Question 9

**(i) Insert an irrational number between **

Sol : 0.4010010001…

**(ii) Find a rational and an irrational number between 2 and 3. How many rational and irrational numbers are there between 2 and 3 ?**

Sol : ,

2.010020003..infinite

**(iii) Find three irrational numbers between 0.2 and 0.32**

Sol :

0.251010010001.. ,

0.252020020002.. ,

0.1030030003..

Category B

#### Question 10

**(i) Write two rational numbers between √3 and √5**

Sol : 1.81 , 1.82

**(ii) Write three rational numbers between √5 and √7**

Sol : 2.51 , 2.52 , 2.53

Category C

#### Question 11

**(i) Find two irrational numbers between √3 and √5**

Sol : √3.1 , √3.2

**(ii) Write three irrational numbers between √5 and √7**

Sol : √5.1 , √5.2 , √5.3

**(iii) Find three irrational numbers between 0.1 and 0.1101**

Sol : 0.1010010001…,

0.1020020002… ,

0.1030030003.. ,

**(iv) Find two rational numbers between 0.01001000100001.. and 0.1001000100001..**

Sol : 0.02 , 0.03

Type 4

#### Question 12

**Represent following irrational numbers on the number line :**

**(i) -√2**

Sol :

**(ii) √5**

Sol :

**(iii) **

Sol :