SELINA Solutions for Class 9 Maths Chapter 1 - Rational and Irrational Numbers

Dive deeper into the intriguing world of numbers with Selina Solutions for ICSE Class 9 Mathematics Chapter 1 Rational and Irrational Numbers. Use the solutions and learn how to figure out whether a number is rational or irrational. TopperLearning’s experts have shared step-by-step answers to get you comfortable with simplifying expressions by using the methods of rationalisation of the denominator.

The Selina textbook covers ample questions for revision of each chapter from your syllabus. You can now use our reference solutions for ICSE Class 9 Maths to understand and learn the methods used by qualified teachers for solving different types of Maths problems. This way, you will be able to equip yourself with the right guidance for answering questions accurately and scoring well in your school exams.

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Chapter 1 - Rational and Irrational Numbers Exercise Ex. 1(B)

Question 1

State, whether the following numbers are rational or not:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iv) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers(v) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers(vi) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 1

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

                      Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 Irrational

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

                      Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Irrational

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Rational

(iv) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersIrrational

(v) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersRational

(vi) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersRational

Question 2

Find the square of:

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 2

 (i)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ii)

 Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

 

Question 3

State, in each case, whether true or false:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iv) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersis an irrational number

(v) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersis a rational number.

(vi) All rational numbers are real numbers.

(vii) All real numbers are rational numbers.

(viii) Some real numbers are rational numbers.

Solution 3

(i) False

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numberswhich is true

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersTrue.

(iv) False because 

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

which is recurring and non-terminating and hence it is rational

(v) True because Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numberswhich is recurring and non-terminating


(vi) True

(vii) False

(viii) True.

Question 4

Given universal set =

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

From the given set, find :

(i) set of rational numbers

(ii) set of irrational numbers

(iii) set of integers

(iv) set of non-negative integers

Solution 4

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

 

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ii) 

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

(iii) 

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

(iv)  

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Question 5

Use method of contradiction to show that Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersand Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersare irrational numbers.

Solution 5

Let us suppose that Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersand Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersare rational numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersand Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers(Where a, b Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers7 and b, y Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers0 x , y)

Squaring both sides

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersa2 and x2 are odd as 3b2 and 5y2 are odd .

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersa and x are odd....(1)

Let a = 3c, x = 5z

a2 = 9c2, x2 = 25z2

3b2 = 9c2, 5y2 = 25z2(From equation Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersb2 =3c2, y2 = 5z2

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersb2 and y2 are odd as 3c2 and 5z2 are odd .

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersb and y are odd...(2)

From equation (1) and (2) we get a, b, x, y are odd integers.

i.e., a, b, and x, y have common factors 3 and 5 this contradicts our assumption that Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersare rational i.e, a, b and x, y do not have any common factors other than.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersis not rational

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersSelina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersand Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersare irrational.

Question 6

Prove that each of the following numbers is irrational:

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 6

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Let Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersbe a rational number.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers = x

Squaring on both the sides, we get

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Here, x is a rational number.

x2 is a rational number. 

x2 - 5 is a rational number.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersis also a rational number.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers is a rational number.

But Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers is an irrational number.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers is an irrational number.

x2- 5 is an irrational number.

x2 is an irrational number. 

x is an irrational number.

But we have assume that x is a rational number.

we arrive at a contradiction.

So, our assumption that Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers is a rational number is wrong.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers is an irrational number.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Let Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersbe a rational number.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers = x

Squaring on both the sides, we get

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Here, x is a rational number.

x2 is a rational number. 

11 - x2 is a rational number.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersis also a rational number.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersis a rational number.

But Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers is an irrational number.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersis an irrational number.

11 - x2 is an irrational number.

x2 is an irrational number. 

x is an irrational number.

But we have assume that x is a rational number.

we arrive at a contradiction.

So, our assumption that Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers is a rational number is wrong.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers is an irrational number.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Let Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers be a rational number.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers = x

Squaring on both the sides, we get

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Here, x is a rational number.

x2 is a rational number. 

9 - x2 is a rational number.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersis also a rational number.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersis a rational number.

But Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers is an irrational number.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersis an irrational number.

9 - x2 is an irrational number.

x2 is an irrational number. 

x is an irrational number.

But we have assume that x is a rational number.

we arrive at a contradiction.

So, our assumption that Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers is a rational number is wrong.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers is an irrational number.

Question 7

Write a pair of irrational numbers whose sum is irrational.

Solution 7

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersare irrational numbers whose sum is irrational.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numberswhich is irrational.

Question 8

Write a pair of irrational numbers whose sum is rational.

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersand Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersare two irrational numbers whose sum is rational.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Question 9

Write a pair of irrational numbers whose difference is irrational.

Solution 9

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersand Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersare two irrational numbers whose difference is irrational.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numberswhich is irrational.

Question 10

Write a pair of irrational numbers whose difference is rational.

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersand Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersare irrational numbers whose difference is rational.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numberswhich is rational.

Question 11

Write a pair of irrational numbers whose product is irrational.

Solution 11

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Question 12

Write in ascending order:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 12

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

and 45 < 48 Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersSelina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

and40 < 54 Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersSelina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersSelina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

and 128 < 147 < 180

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersSelina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Question 13

Write in ascending order:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 13

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

and 45 < 48 Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersSelina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

and40 < 54 Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersSelina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersSelina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

and 128 < 147 < 180

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersSelina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Question 14

Write in descending order:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 14

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Since 162 > 96

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

141 > 63 Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersSelina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Question 15

Compare.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 15

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersand Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Make powers Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersand Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numberssame

L.C.M. of 6,4 is 12

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

and Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersand Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

L.C.M. of 2 and 3 is 6.

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers, Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

Question 16

Insert two irrational numbers between 5 and 6.

Solution 16

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

Question 17

Insert five irrational numbers between Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersand Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers.

Solution 17

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Question 18

Write two rational numbers between Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 18

We want rational numbers a/b and c/d such that: Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers< a/b < c/d < Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Consider any two rational numbers between 2 and 3 such that they are perfect squares.

Let us take 2.25 and 2.56 as Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Thus we have,

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers



Question 19

Write three rational numbers between Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 19

Consider some rational numbers between 3 and 5 such that they are perfect squares.

Let us take, 3.24, 3.61, 4, 4.41 and 4.84 as

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Question 20(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 20(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Question 20(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 20(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Question 20(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 20(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Question 20(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 20(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Chapter 1 - Rational and Irrational Numbers Exercise Ex. 1(C)

Question 1

State, with reasons, which of the following are surds and which are not:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iv) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(v) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(vi) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(vii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(viii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 1

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersWhich is irrational

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersis a surd

 

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersWhich is irrational

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers is a surd

 

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersis a surd

 

(iv) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numberswhich is rational

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersis not a surd

 

(v) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational NumbersSelina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersis not a surd

 

(vi) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers= -5

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersis is not a surd

(vii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersnot a surd as Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers is irrational

 

(viii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersis not a surd because Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers is irrational.

Question 2

Write the lowest rationalising factor of:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iv) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(v) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(vi) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(vii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(viii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ix) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers


 

Solution 2

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numberswhich is rational

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numberslowest rationalizing factor is Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numberslowest rationalizing factor is Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

(iii)  Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numberslowest rationalizing factor is Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

(iv) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Therefore, lowest rationalizing factor is Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

(v) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numberslowest rationalizing factor is Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

  (vi) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Therefore lowest rationalizing factor is Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 
 (vii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Its lowest rationalizing factor is Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(viii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Its lowest rationalizing factor is Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 (ix) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

its lowest rationalizing factor is Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

Question 3

Rationalise the denominators of :

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iv) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(v) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(vi) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(vii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(viii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ix) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

Solution 3

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 (iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 (v)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 (vi)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 (vii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(viii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 (ix)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

Question 4

Find the values of 'a' and 'b' in each of the following:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iv) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 4

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 (ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 (iv) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

Question 5

Simplify:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 5

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers


(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Question 6

If x = Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbersand y = Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers; find:

(i) x2     (ii) y2

(iii) xy   (iv) x2 + y2 + xy.

 

Solution 6

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

 

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

 

(iii) xy = Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

(iv) x2 + y2 + xy = 161 - Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

= 322 + 1 = 323

 

 

 

Question 7

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

(i) m

(ii) n2

(iii) mn

Solution 7

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Question 8

If x = 2Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers+ 2Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers, find:

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 8

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

Question 9

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

 

 

 

Solution 9

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

 

 

 

 

 

 

 

 

 

 

 

 

Question 10

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

 

 

 

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Question 11

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 11

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Question 12

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 12

 Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Question 13(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 13(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Question 13(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 13(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Question 14

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 14

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Question 15

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 15

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Chapter 1 - Rational and Irrational Numbers Exercise Ex. 1(A)

Question 1

Is zero a rational number? Can it be written in the form Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers, where p and q are integers and q≠0?

Solution 1

Yes, zero is a rational number.

As it can be written in the form of Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers, where p and q are integers and q≠0?

0 = Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Question 2

Are the following statements true or false? Give reasons for your answers.

i. Every whole number is a natural number.

ii. Every whole number is a rational number.

iii. Every integer is a rational number.

iv. Every rational number is a whole number.

Solution 2

i. False, zero is a whole number but not a natural number.

ii. True, Every whole can be written in the form of Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers, where p and q are integers and q≠0.

iii. True, Every integer can be written in the form of Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers, where p and q are integers and q≠0.

iv. False.

Example: Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers is a rational number, but not a whole number.

Question 3

Arrange Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers  in ascending order of their magnitudes.

Also, find the difference between the largest and smallest of these fractions. Express this difference as a decimal fraction correct to one decimal place.

Solution 3

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Question 4

Arrange Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers  in descending order of their

 

 

 

magnitudes.

Also, find the sum of the lowest and largest of these fractions. Express the result obtained as a decimal fraction correct to two decimal places.

Solution 4

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Question 5(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 5(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Question 5(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 5(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Question 5(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 5(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Question 5(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 5(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Question 5(v)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 5(v)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Question 5(vi)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 5(vi)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Question 5(vii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 5(vii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers 

Question 5(viii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers

Solution 5(viii)

Selina Solutions Icse Class 9 Mathematics Chapter - Rational And Irrational Numbers