#### Chapters

Chapter 2 : Exponents of Real Numbers

Chapter 3 : Rationalisation

Chapter 4 : Algebraic Identities

Chapter 5 : Factorisation of Algebraic Expressions

Chapter 6 : Factorisation of Polynomials

Chapter 7 : Introduction to Euclid’s Geometry

Chapter 8 : Lines and Angles

Chapter 9 : Triangle and its Angles

Chapter 10 : Congruent Triangles

Chapter 11 : Co-ordinate Geometry

Chapter 12 : Heron’s Formula

Chapter 13 : Linear Equations in Two Variables

Chapter 14 : Quadrilaterals

Chapter 15 : Areas of Parallelograms and Triangles

Chapter 16 : Circles

Chapter 17 : Constructions

Chapter 18 : Surface Areas and Volume of a Cuboid and Cube

Chapter 19 : Surface Areas and Volume of a Circular Cylinder

Chapter 20 : Surface Areas and Volume of A Right Circular Cone

Chapter 21 : Surface Areas and Volume of a Sphere

Chapter 22 : Tabular Representation of Statistical Data

Chapter 23 : Graphical Representation of Statistical Data

Chapter 24 : Measures of Central Tendency

Chapter 25 : Probability

## Chapter 3 : Rationalisation

#### Pages 0 - 3

Simplify of the following:

`root(3)4 xx root(3)16`

Simplify of the following:

`root(4)1250/root(4)2`

Simplify the following expressions:

`(4 + sqrt7)(3 + sqrt2)`

Simplify the following expressions:

`(3 + sqrt3)(5 - sqrt2)`

Simplify the following expressions:

`(sqrt5 - 2)(sqrt3 - sqrt5)`

Simplify the following expressions:

`(11 + sqrt11)(11 - sqrt11)`

Simplify the following expressions:

`(5 + sqrt7)(5 - sqrt7)`

Simplify the following expressions:

`(sqrt8 - sqrt2)(sqrt8 + sqrt2)`

Simplify the following expressions:

`(3 + sqrt3)(3 - sqrt3)`

Simplify the following expressions:

`(sqrt5 - sqrt2)(sqrt5 + sqrt2)`

Simplify the following expressions:

`(sqrt3 + sqrt7)^2`

Simplify the following expressions:

`(sqrt5 - sqrt3)^2`

Simplify the following expressions:

`(2sqrt5 + 3sqrt2)^2`

#### Pages 13 - 15

Rationalise the denominator of each of the following

`3/sqrt5`

Rationalise the denominator of each of the following

`3/(2sqrt5)`

Rationalise the denominator of each of the following

`1/sqrt12`

Rationalise the denominator of the following

`sqrt2/sqrt5`

Rationalise the denominator of each of the following

`(sqrt3 + 1)/sqrt2`

Rationalise the denominator of the following

`(sqrt2 + sqrt5)/3`

Rationalise the denominator of the following

`(3sqrt2)/sqrt5`

Find the value to three places of decimals of the following. It is given that

`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`

`2/sqrt3`

Find the value to three places of decimals of the following. It is given that

`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`

`3/sqrt10`

Find the value to three places of decimals of the following. It is given that

`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`

`(sqrt5 + 1)/sqrt2`

Find the value to three places of decimals of the following. It is given that

`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`

`(sqrt10 + sqrt15)/sqrt2`

`

Find the value to three places of decimals of the following. It is given that

`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`

`(2 + sqrt3)/3`

Find the value to three places of decimals of the following. It is given that

`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`

`(sqrt2 - 1)/sqrt5`

Express the following with rational denominator:

`1/(3 + sqrt2)`

Express of the following with rational denominator:

`1/(sqrt6 - sqrt5)`

Express the following with rational denominator:

`16/(sqrt41 - 5)`

Express the following with rational denominator:

`30/(5sqrt3 - 3sqrt5)`

Express the following with rational denominator:

`1/(2sqrt5 - sqrt3)`

Express the following with rational denominator:

`(sqrt3 + 1)/(2sqrt2 - sqrt3)`

Express the following with rational denominator:

`(6 - 4sqrt2)/(6 + 4sqrt2)`

Express the following with rational denominator:

`(3sqrt2 + 1)/(2sqrt5 - 3)`

Express each one of the following with rational denominator:

`(b^2)/(sqrt(a^2 + b^2) + a)`

Rationales the denominator and simplify:

`(3 - sqrt2)/(3 + sqrt2)`

Rationales the denominator and simplify:

`(5 + 2sqrt3)/(7 + 4sqrt3)`

Rationales the denominator and simplify:

`(1 + sqrt2)/(3 - 2sqrt2)`

Rationales the denominator and simplify:

`(4sqrt3 + 5sqrt2)/(sqrt48 + sqrt18)`

Rationales the denominator and simplify:

`(2sqrt3 - sqrt5)/(2sqrt2 + 3sqrt3)`

Rationales the denominator and simplify:

`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`

Simplify:

`(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)`

Simplify

`1/(2 + sqrt3) + 2/(sqrt5 - sqrt3) + 1/(2 - sqrt5)`

Simplify

`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) + 3/(sqrt5 + sqrt2)`

In the following determine rational numbers *a* and *b*:

`(sqrt3 - 1)/(sqrt3 + 1) = a - bsqrt3`

In the following determine rational numbers *a* and *b*:

`(4 + sqrt2)/(2 + sqrt2) = n - sqrtb`

In the following determine rational numbers *a* and *b*:

`(3 + sqrt2)/(3 - sqrt2) = a + bsqrt2`

In the following determine rational numbers *a* and *b*:

`(5 + 3sqrt3)/(7 + 4sqrt3) = a + bsqrt3`

In the following determine rational numbers *a* and *b*:

`(sqrt11 - sqrt7)/(sqrt11 + sqrt7) = a - bsqrt77`

In the following determine rational numbers *a* and *b*:

`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`

Find the value of `6/(sqrt5 - sqrt3)` it being given that `sqrt3 = 1.732` and `sqrt5 = 2.236`

Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`

`(3 - sqrt5)/(3 + 2sqrt5)`

Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`

`(1 + sqrt2)/(3 - 2sqrt2)`

if `x = 2 + sqrt3`,find the value of `x^2 + 1/x^2`

if `x= 3 + sqrt8`, find the value of `x^2 + 1/x^2`

if `x = (sqrt3 + 1)/2` find the value of `4x^2 +2x^2 - 8x + 7`

#### Textbook solutions for Class 9

## RD Sharma solutions for Class 9 Mathematics chapter 3 - Rationalisation

RD Sharma solutions for Class 9 Maths chapter 3 (Rationalisation) 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 CBSE Mathematics for Class 9 by R D Sharma (2018-19 Session) solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 9 Mathematics chapter 3 Rationalisation are Introduction of Real Number, Irrational Numbers, Real Numbers and Their Decimal Expansions, Representing Real Numbers on the Number Line, Operations on Real Numbers, Laws of Exponents for Real Numbers.

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