#### Chapters

Chapter 2: Compound Interest (Without using formula)

Chapter 3: Compound Interest (Using Formula)

Chapter 4: Expansions (Including Substitution)

Chapter 5: Factorisation

Chapter 6: Simultaneous (Linear) Equations (Including Problems)

Chapter 7: Indices (Exponents)

Chapter 8: Logarithms

Chapter 9: Triangles [Congruency in Triangles]

Chapter 10: Isosceles Triangles

Chapter 11: Inequalities

Chapter 12: Mid-point and Its Converse [ Including Intercept Theorem]

Chapter 13: Pythagoras Theorem [Proof and Simple Applications with Converse]

Chapter 14: Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]

Chapter 15: Construction of Polygons (Using ruler and compass only)

Chapter 16: Area Theorems [Proof and Use]

Chapter 17: Circle

Chapter 18: Statistics

Chapter 19: Mean and Median (For Ungrouped Data Only)

Chapter 20: Area and Perimeter of Plane Figures

Chapter 21: Solids [Surface Area and Volume of 3-D Solids]

Chapter 22: Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and their Reciprocals]

Chapter 23: Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]

Chapter 24: Solution of Right Triangles [Simple 2-D Problems Involving One Right-angled Triangle]

Chapter 25: Complementary Angles

Chapter 26: Co-ordinate Geometry

Chapter 27: Graphical Solution (Solution of Simultaneous Linear Equations, Graphically)

Chapter 28: Distance Formula

## Chapter 1: Rational and Irrational Numbers

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

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

- Every whole number is a natural number.
- Every whole number is a rational number.
- Every integer is a rational number.
- Every rational number is a whole number.

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

**State, whether the following number is rational or not :**

`( [√7]/[6sqrt2])^2`

**Find the square of :** `[3sqrt5]/5`

**Find the square of : **√3 + √2

**Find the square of : **√5 - 2

**Find the square of :** 3 + 2√5

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

True

False

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

True

False

**State, in each case, whether true or false :**** **

3√7 - 2√7 = √7

True

False

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

True

False

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

True

False

**State, in each case, whether true or false :**** **

All rational numbers are real numbers.

True

False

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

True

False

**State, in each case, whether true or false :**** **

Some real numbers are rational numbers.

True

False

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

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

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

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

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

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

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

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

Write a pair of irrational numbers whose sum is irrational.

Write a pair of irrational numbers whose sum is rational.

Write a pair of irrational numbers whose difference is irrational.

Write a pair of irrational numbers whose difference is rational.

Write a pair of irrational numbers whose product is irrational.

Write a pair of irrational numbers whose product is rational.

**Write in ascending order: **3√5 and 4√3

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

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

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

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

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

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

**Compare :** `sqrt24 and root(3)(35)`

Insert two irrational numbers between 5 and 6.

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

Write two rational numbers between √2 and √3.

Write three rational numbers between √3 and √5.

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

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

**Simplify :** ( 3 + √2 )( 4 + √7 )

**Simplify :** (√3 - √2 )^{2}

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

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

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

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

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

`root(3)(64)`

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

`root(3)(25). root(3)(40)`

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

`root(3)( -125 )`

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

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

`sqrt( 3 + sqrt2 )`

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

**Write the lowest rationalising factor of : **√24

**Write the lowest rationalising factor of : **√5 - 3

**Write the lowest rationalising factor of : **7 - √7

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

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

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

**Write the lowest rationalising factor of : **√13 + 3

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

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

**Rationalise the denominators of :** `3/sqrt5`

**Rationalise the denominators of : **`(2sqrt3)/sqrt5`

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

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

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

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

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

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

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

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

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

`( sqrt7 - 2 )/( sqrt7 + 2 ) = asqrt7 + b`

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

`3/[ sqrt3 - sqrt2 ] = asqrt3 - bsqrt2`

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

`[5 + 3sqrt2]/[ 5 - 3sqrt2] = a + bsqrt2`

**Simplify :**

` 22/[2sqrt3 + 1] + 17/[ 2sqrt3 - 1]`

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

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

x^{2}

**If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find : **y^{2}

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

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

x^{2} + y^{2} + xy.

If m = `1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ],` find m^{2}

If m = `1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ],` find n^{2}

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

If x = 2√3 + 2√2 , find : `1/x`

If x = 2√3 + 2√2 , find : `(x + 1/x)`

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

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

If x = 5 - 2√6, find `x^2 + 1/x^2`

**Show that :**

`1/[ 3 - 2√2] - 1/[ 2√2 - √7 ] + 1/[ √7 - √6 ] - 1/[ √6 - √5 ] + 1/[√5 - 2] = 5`

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

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

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

**Simplify** : `(2 - √3)/(√3)`

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

If `[ 2 + √5 ]/[ 2 - √5] = x and [2 - √5 ]/[ 2 + √5] = y`; find the value of x^{2} - y^{2}.

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

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

## Chapter 1: Rational and Irrational Numbers

## 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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