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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) \sqrt{\dfrac{25}{169}} is a rational number

Sol : False

\dfrac{\sqrt{25}}{\sqrt{169}}=\sqrt{\dfrac{5times5}{13\times 13}} =\sqrt{\dfrac{5^2}{13^2}}=\dfrac{5}{13} = rational number

 

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

Sol : False, =\dfrac{3}{2} 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 \dfrac{8}{27} is __

Sol : 0.\overline{296}

 

(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) \sqrt{47}

Sol : Irrational

 

(ii) \sqrt{19}

Sol : Irrational

 

(iii) \sqrt{576}

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) \sqrt{\dfrac{36}{64}}

Sol:

 

(ii) √3

Sol:

 

(iii)  -\dfrac{9}{\sqrt{49}}

Sol:

 

(iv)  \dfrac{9}{81}

Sol:

 


Question 7

Which of the following number is not irrational ?

(i) \dfrac{2}{\sqrt{3}},\dfrac{\sqrt{3}}{4},\sqrt{\dfrac{25}{49}},7\sqrt{2}

Sol: =\sqrt{\dfrac{25}{49}}=\dfrac{5}{7}

 

(ii) \dfrac{3}{\sqrt{2}},\dfrac{1}{2},\sqrt{3},\sqrt{11}

Sol: =\dfrac{1}{2}

 


Question 8

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

(i) \sqrt{\dfrac{81}{625}} , \sqrt{\dfrac{625}{325}},\sqrt{\dfrac{5}{196}}

Sol : =\sqrt{\dfrac{81}{625}}=\dfrac{9}{25}

 

(ii) \sqrt{7},3\sqrt{7},\sqrt[4]{\dfrac{25}{256}},\sqrt{33}

Sol : \sqrt[4]{\dfrac{25}{256}}

 


Category A

Question 9

(i) Insert an irrational number between \dfrac{1}{3}\text{ and }\dfrac{1}{2}

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 : \dfrac{5}{2} ,

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) -\dfrac{\sqrt{3}}{2}

Sol :

 


 

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