# KC Sinha Mathematics Solution Class 9 Chapter 1 Real numbers exercise 1.2

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) x2=15

Sol: x represents an irrational number

(ii) y2=16

Sol: y represents a rational number

(iii) z2=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 :

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