# Selina solutions for Concise Mathematics Class 9 ICSE chapter 1 - Rational and Irrational Numbers [Latest edition]

## Chapter 1: Rational and Irrational Numbers

Exercise 1 (A)Exercise 1 (B)Exercise 1 (C)Exercise 1 (D)
Exercise 1 (A) [Page 4]

### Selina solutions for Concise Mathematics Class 9 ICSE Chapter 1 Rational and Irrational Numbers Exercise 1 (A) [Page 4]

Exercise 1 (A) | Q 1 | Page 4

Is zero a rational number ? Can it be written in the form P/q, where p and q are integers and q≠0 ?

Exercise 1 (A) | Q 2 | Page 4

Are the following statement true or false ? Give reason for your answer.

1. Every whole number is a natural number.
2. Every whole number is a rational number.
3. Every integer is a rational number.
4. Every rational number is a whole number.
Exercise 1 (A) | Q 3 | Page 4

Arrange -5/7, 7/12, -2/3 and 11/18 in ascending order of their magnitudes.
Also, find the difference between the largest and smallest of these rational numbers. Express this difference as a decimal fraction correct to one decimal place.

Exercise 1 (A) | Q 4 | Page 4

Arrange 5/8, -3/16, -1/4 and 17/32 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.

Exercise 1 (A) | Q 5.1 | Page 4

Without doing any actual division, find which of the following rational numbers have terminating decimal representation : 7/16

Exercise 1 (A) | Q 5.2 | Page 4

Without doing any actual division, find which of the following rational numbers have terminating decimal representation : 23/125

Exercise 1 (A) | Q 5.3 | Page 4

Without doing any actual division, find which of the following rational numbers have terminating decimal representation : 9/14

Exercise 1 (A) | Q 5.4 | Page 4

Without doing any actual division, find which of the following rational numbers have terminating decimal representation : 32/45

Exercise 1 (A) | Q 5.5 | Page 4

Without doing any actual division, find which of the following rational numbers have terminating decimal representation : 43/50

Exercise 1 (A) | Q 5.6 | Page 4

Without doing any actual division, find which of the following rational numbers have terminating decimal representation : 17/40

Exercise 1 (A) | Q 5.7 | Page 4

Without doing any actual division, find which of the following rational numbers have terminating decimal representation : 61/75

Exercise 1 (A) | Q 5.8 | Page 4

Without doing any actual division, find which of the following rational numbers have terminating decimal representation : 123/250

Exercise 1 (B) [Pages 13 - 14]

### Selina solutions for Concise Mathematics Class 9 ICSE Chapter 1 Rational and Irrational Numbers Exercise 1 (B) [Pages 13 - 14]

Exercise 1 (B) | Q 1.1 | Page 13

State, whether the following numbers is rational or not : ( 2 + √2 )2

Exercise 1 (B) | Q 1.2 | Page 13

State, whether the following numbers is rational or not : ( 3 - √3 )2

Exercise 1 (B) | Q 1.3 | Page 13

State, whether the following numbers is rational or not : ( 5 + √5 )( 5 - √5 )

Exercise 1 (B) | Q 1.4 | Page 13

State, whether the following numbers is rational or not : ( √3 - √2 )2

Exercise 1 (B) | Q 1.5 | Page 13

State, whether the following numbers is rational or not :
( 3/[2sqrt2])^2

Exercise 1 (B) | Q 1.6 | Page 13

State, whether the following number is rational or not :
( [√7]/[6sqrt2])^2

Exercise 1 (B) | Q 2.1 | Page 13

Find the square of : [3sqrt5]/5

Exercise 1 (B) | Q 2.2 | Page 13

Find the square of : √3 + √2

Exercise 1 (B) | Q 2.3 | Page 13

Find the square of : √5 - 2

Exercise 1 (B) | Q 2.4 | Page 13

Find the square of : 3 + 2√5

Exercise 1 (B) | Q 3.1 | Page 13

State, in each case, whether true or false :
√2 + √3 = √5

• True

• False

Exercise 1 (B) | Q 3.2 | Page 13

State, in each case, whether true or false :
2√4 + 2 = 6

• True

• False

Exercise 1 (B) | Q 3.3 | Page 13

State, in each case, whether true or false :
3√7 - 2√7 = √7

• True

• False

Exercise 1 (B) | Q 3.4 | Page 13

State, in each case, whether true or false :
2/7 ia an irrational number.

• True

• False

Exercise 1 (B) | Q 3.5 | Page 13

State, in each case, whether true or false :
5/11 is a rational number.

• True

• False

Exercise 1 (B) | Q 3.6 | Page 13

State, in each case, whether true or false :
All rational numbers are real numbers.

• True

• False

Exercise 1 (B) | Q 3.7 | Page 13

State, in each case, whether true or false :
All real numbers are rational numbers.

• True

• False

Exercise 1 (B) | Q 3.8 | Page 13

State, in each case, whether true or false :
Some real numbers are rational numbers.

• True

• False

Exercise 1 (B) | Q 4.1 | Page 14

Given universal set =
{ -6, -5 3/4, -sqrt4, -3/5, -3/8, 0, 4/5, 1, 1 2/3, sqrt8, 3.01, π, 8.47 }
From the given set, find :  set of rational numbers

Exercise 1 (B) | Q 4.2 | Page 14

Given universal set =
{ -6, -5 3/4, -sqrt4, -3/5, -3/8, 0, 4/5, 1, 1 2/3, sqrt8, 3.01, π, 8.47 }
From the given set, find : set of irrational numbers

Exercise 1 (B) | Q 4.3 | Page 14

Given universal set =
{ -6, -5 3/4, -sqrt4, -3/5, -3/8, 0, 4/5, 1, 1 2/3, sqrt8, 3.01, π, 8.47 }
From the given set, find : set of integers

Exercise 1 (B) | Q 4.4 | Page 14

Given universal set =
{ -6, -5 3/4, -sqrt4, -3/5, -3/8, 0, 4/5, 1, 1 2/3, sqrt8, 3.01, π, 8.47 }
From the given set, find : set of non-negative integers

Exercise 1 (B) | Q 5 | Page 14

Use method of contradiction to show that √3 and √5 are irrational numbers.

Exercise 1 (B) | Q 6.1 | Page 14

Prove that the following number is irrational: √3 + √2

Exercise 1 (B) | Q 6.2 | Page 14

Prove that the following number is irrational:  3 - √2

Exercise 1 (B) | Q 6.3 | Page 14

Prove that the following number is irrational: √5 - 2

Exercise 1 (B) | Q 7 | Page 14

Write a pair of irrational numbers whose sum is irrational.

Exercise 1 (B) | Q 8 | Page 14

Write a pair of irrational numbers whose sum is rational.

Exercise 1 (B) | Q 9 | Page 14

Write a pair of irrational numbers whose difference is irrational.

Exercise 1 (B) | Q 10 | Page 14

Write a pair of irrational numbers whose difference is rational.

Exercise 1 (B) | Q 11 | Page 14

Write a pair of irrational numbers whose product is irrational.

Exercise 1 (B) | Q 12 | Page 14

Write a pair of irrational numbers whose product is rational.

Exercise 1 (B) | Q 13.1 | Page 14

Write in ascending order: 3√5 and 4√3

Exercise 1 (B) | Q 13.2 | Page 14

Write in ascending order :  2 root(3)(5)  and 3 root(3)(2)

Exercise 1 (B) | Q 13.3 | Page 14

Write in ascending order :  6√5, 7√3 and 8√2

Exercise 1 (B) | Q 13.3 | Page 14

Write in ascending order : 6√5, 7√3, and 8√2

Exercise 1 (B) | Q 14.1 | Page 14

Write in descending order: 2 root(3)(6) and 3 root(4)(2)

Exercise 1 (B) | Q 14.2 | Page 14

Write in descending order: 7√3 and 3√7

Exercise 1 (B) | Q 15.1 | Page 14

Compare : root(6)(15) and root(4)(12)

Exercise 1 (B) | Q 15.2 | Page 14

Compare : sqrt24 and root(3)(35)

Exercise 1 (B) | Q 16 | Page 14

Insert two irrational numbers between 5 and 6.

Exercise 1 (B) | Q 17 | Page 14

Insert five irrational numbers between 2√5 and 3√3.

Exercise 1 (B) | Q 18 | Page 14

Write two rational numbers between √2 and √3.

Exercise 1 (B) | Q 19 | Page 14

Write three rational numbers between √3 and √5.

Exercise 1 (B) | Q 20.1 | Page 14

Simplify : root(5)(16) xx root(5)(2)

Exercise 1 (B) | Q 20.2 | Page 14

Simplify : root(4)(243)/root(4)(3)

Exercise 1 (B) | Q 20.3 | Page 14

Simplify : ( 3 + √2 )( 4 + √7 )

Exercise 1 (B) | Q 20.4 | Page 14

Simplify : (√3 - √2 )2

Exercise 1 (C) [Pages 21 - 22]

### Selina solutions for Concise Mathematics Class 9 ICSE Chapter 1 Rational and Irrational Numbers Exercise 1 (C) [Pages 21 - 22]

Exercise 1 (C) | Q 1.1 | Page 21

State, with reason, of the following is surd or not : √180

Exercise 1 (C) | Q 1.2 | Page 21

State, with reason, of the following is surd or not :
root(4)(27)

Exercise 1 (C) | Q 1.3 | Page 21

State, with reason, of the following is surd or not :
root(5)(128)

Exercise 1 (C) | Q 1.4 | Page 21

State, with reason, of the following is surd or not :
root(3)(64)

Exercise 1 (C) | Q 1.5 | Page 21

State, with reason, of the following is surd or not :
root(3)(25). root(3)(40)

Exercise 1 (C) | Q 1.6 | Page 21

State, with reason, of the following is surd or not :
root(3)( -125 )

Exercise 1 (C) | Q 1.7 | Page 21

State, with reason, of the following is surd or not : √π

Exercise 1 (C) | Q 1.8 | Page 21

State, with reason, of the following is surd or not :
sqrt( 3 + sqrt2 )

Exercise 1 (C) | Q 2.1 | Page 21

Write the lowest rationalising factor of : 5√2

Exercise 1 (C) | Q 2.2 | Page 21

Write the lowest rationalising factor of : √24

Exercise 1 (C) | Q 2.3 | Page 21

Write the lowest rationalising factor of : √5 - 3

Exercise 1 (C) | Q 2.4 | Page 21

Write the lowest rationalising factor of : 7 - √7

Exercise 1 (C) | Q 2.5 | Page 21

Write the lowest rationalising factor of : √18 - √50

Exercise 1 (C) | Q 2.6 | Page 21

Write the lowest rationalising factor of : √5 - √2

Exercise 1 (C) | Q 2.6 | Page 21

Rationalise the denominators of : [ √3 + 1 ]/[ √3 - 1 ]

Exercise 1 (C) | Q 2.7 | Page 21

Write the lowest rationalising factor of : √13 + 3

Exercise 1 (C) | Q 2.8 | Page 21

Write the lowest rationalising factor of : 15 - 3√2

Exercise 1 (C) | Q 2.9 | Page 21

Write the lowest rationalising factor of : 3√2 + 2√3

Exercise 1 (C) | Q 3.1 | Page 21

Rationalise the denominators of : 3/sqrt5

Exercise 1 (C) | Q 3.2 | Page 21

Rationalise the denominators of : (2sqrt3)/sqrt5

Exercise 1 (C) | Q 3.3 | Page 21

Rationalise the denominators of : 1/(sqrt3 - sqrt2 )

Exercise 1 (C) | Q 3.4 | Page 21

Rationalise the denominators of : 3/[ sqrt5 + sqrt2 ]

Exercise 1 (C) | Q 3.5 | Page 21

Rationalise the denominators of : [ 2 - √3 ]/[ 2 + √3 ]

Exercise 1 (C) | Q 3.6 | Page 21

Rationalise the denominators of : [ sqrt3 + 1 ]/[ sqrt3 - 1]

Exercise 1 (C) | Q 3.7 | Page 21

Rationalise the denominators of : [ sqrt3 - sqrt2 ]/[ sqrt3 + sqrt2 ]

Exercise 1 (C) | Q 3.8 | Page 21

Rationalise the denominators of : [sqrt6 - sqrt5]/[sqrt6 + sqrt5]

Exercise 1 (C) | Q 3.9 | Page 21

Rationalise the denominators of : [ 2√5 + 3√2 ]/[ 2√5 - 3√2 ]

Exercise 1 (C) | Q 4.1 | Page 21

Find the values of 'a' and 'b' in each of the following :
[2 + sqrt3]/[ 2 - sqrt3 ] = a + bsqrt3

Exercise 1 (C) | Q 4.2 | Page 21

Find the values of 'a' and 'b' in each of the following:
( sqrt7 - 2 )/( sqrt7 + 2 ) = asqrt7 + b

Exercise 1 (C) | Q 4.3 | Page 21

Find the values of 'a' and 'b' in each of the following:
3/[ sqrt3 - sqrt2 ] = asqrt3 - bsqrt2

Exercise 1 (C) | Q 4.4 | Page 21

Find the values of 'a' and 'b' in each of the following:
[5 + 3sqrt2]/[ 5 - 3sqrt2] = a + bsqrt2

Exercise 1 (C) | Q 5.1 | Page 21

Simplify :
 22/[2sqrt3 + 1] + 17/[ 2sqrt3 - 1]

Exercise 1 (C) | Q 5.2 | Page 21

Simplify :
sqrt2/[sqrt6 - sqrt2] - sqrt3/[sqrt6 + sqrt2]

Exercise 1 (C) | Q 6.1 | Page 21

If x =[sqrt5 - 2 ]/[ sqrt5 + 2] and y = [ sqrt5 + 2]/[ sqrt5 - 2 ]; find :
x2

Exercise 1 (C) | Q 6.2 | Page 21

If x =[sqrt5 - 2 ]/[ sqrt5 + 2] and y = [ sqrt5 + 2]/[ sqrt5 - 2 ]; find : y2

Exercise 1 (C) | Q 6.3 | Page 22

If x =[sqrt5 - 2 ]/[ sqrt5 + 2] and y = [ sqrt5 + 2]/[ sqrt5 - 2 ]; find :  xy

Exercise 1 (C) | Q 6.4 | Page 22

If x =[sqrt5 - 2 ]/[ sqrt5 + 2] and y = [ sqrt5 + 2]/[ sqrt5 - 2 ]; find :
x2 + y2 + xy.

Exercise 1 (C) | Q 7.1 | Page 22

If m = 1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ], find m2

Exercise 1 (C) | Q 7.2 | Page 22

If m = 1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ], find n2

Exercise 1 (C) | Q 7.2 | Page 22

If m = 1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ], find mn

Exercise 1 (C) | Q 8.1 | Page 22

If x = 2√3 + 2√2 , find : 1/x

Exercise 1 (C) | Q 8.2 | Page 22

If x = 2√3 + 2√2 , find : (x + 1/x)

Exercise 1 (C) | Q 8.3 | Page 22

If x = 2√3 + 2√2 , find : ( x + 1/x)^2

Exercise 1 (C) | Q 9 | Page 22

If x = 1 - √2, find the value of ( x - 1/x )^3

Exercise 1 (C) | Q 10 | Page 22

If x = 5 - 2√6, find x^2 + 1/x^2

Exercise 1 (C) | Q 11 | Page 22

Show that :
1/[ 3 - 2√2] - 1/[ 2√2 - √7 ] + 1/[ √7 - √6 ] - 1/[ √6 - √5 ] + 1/[√5 - 2] = 5

Exercise 1 (C) | Q 12 | Page 22

Rationalise the denominator of : 1/[ √3 - √2 + 1]

Exercise 1 (C) | Q 13.1 | Page 22

If √2 = 1.4 and √3 = 1.7, find the value of : 1/(√3 - √2)

Exercise 1 (C) | Q 13.2 | Page 22

If √2 = 1.4 and √3 = 1.7, find the value of : 1/(3 + 2√2)

Exercise 1 (C) | Q 13.3 | Page 22

Simplify : (2 - √3)/(√3)

Exercise 1 (C) | Q 14 | Page 22

Evaluate : ( 4 - √5 )/( 4 + √5 ) + ( 4 + √5 )/( 4 - √5 )

Exercise 1 (C) | Q 15 | Page 22

If [ 2 + √5 ]/[ 2 - √5] = x and  [2 - √5 ]/[ 2 + √5] = y; find the value of x2 - y2.

Exercise 1 (D) [Page 22]

### Selina solutions for Concise Mathematics Class 9 ICSE Chapter 1 Rational and Irrational Numbers Exercise 1 (D) [Page 22]

Exercise 1 (D) | Q 1 | Page 22

Simplify : sqrt18/[ 5sqrt18 + 3sqrt72 - 2sqrt162]

## Chapter 1: Rational and Irrational Numbers

Exercise 1 (A)Exercise 1 (B)Exercise 1 (C)Exercise 1 (D)

## Selina solutions for Concise Mathematics Class 9 ICSE chapter 1 - Rational and Irrational Numbers

Selina solutions for Concise Mathematics Class 9 ICSE chapter 1 (Rational and Irrational Numbers) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Concise Mathematics Class 9 ICSE solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Concise Mathematics Class 9 ICSE chapter 1 Rational and Irrational Numbers are Concept of Rational Numbers, Properties of Rational Numbers, Decimal Representation of Rational Numbers, Concept of Irrational Numbers, Concept of Real Numbers, Concept of Surds, Rationalisation of Surds, Simplifying an expression by rationalization of the Denominator.

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