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# RD Sharma solutions for Mathematics for Class 9 chapter 3 - Rationalisation [Latest edition]

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## Chapter 3: Rationalisation

Ex. 3.1Ex. 3.2Others

#### RD Sharma solutions for Mathematics for Class 9 Chapter 3 Rationalisation Exercise 3.1 [Pages 2 - 3]

Ex. 3.1 | Q 1.1 | Page 2

Simplify of the following:

root(3)4  xx root(3)16

Ex. 3.1 | Q 1.2 | Page 2

Simplify of the following:

root(4)1250/root(4)2

Ex. 3.1 | Q 2.1 | Page 2

Simplify the following expressions:

(4 + sqrt7)(3 + sqrt2)

Ex. 3.1 | Q 2.2 | Page 2

Simplify the following expressions:

(3 + sqrt3)(5 - sqrt2)

Ex. 3.1 | Q 2.3 | Page 2

Simplify the following expressions:

(sqrt5 - 2)(sqrt3 - sqrt5)

Ex. 3.1 | Q 3.1 | Page 2

Simplify the following expressions:

(11 + sqrt11)(11 - sqrt11)

Ex. 3.1 | Q 3.2 | Page 2

Simplify the following expressions:

(5 + sqrt7)(5 - sqrt7)

Ex. 3.1 | Q 3.3 | Page 2

Simplify the following expressions:

(sqrt8 - sqrt2)(sqrt8 + sqrt2)

Ex. 3.1 | Q 3.4 | Page 2

Simplify the following expressions:

(3 + sqrt3)(3 - sqrt3)

Ex. 3.1 | Q 3.5 | Page 2

Simplify the following expressions:

(sqrt5 - sqrt2)(sqrt5 + sqrt2)

Ex. 3.1 | Q 4.1 | Page 3

Simplify the following expressions:

(sqrt3 + sqrt7)^2

Ex. 3.1 | Q 4.2 | Page 3

Simplify the following expressions:

(sqrt5 - sqrt3)^2

Ex. 3.1 | Q 4.3 | Page 3

Simplify the following expressions:

(2sqrt5 + 3sqrt2)^2

#### RD Sharma solutions for Mathematics for Class 9 Chapter 3 Rationalisation Exercise 3.2 [Pages 14 - 15]

Ex. 3.2 | Q 1.1 | Page 14

Rationalise the denominator of each of the following

3/sqrt5

Ex. 3.2 | Q 1.2 | Page 14

Rationalise the denominator of the following:

3/(2sqrt5)

Ex. 3.2 | Q 1.3 | Page 14

Rationalise the denominator of each of the following

1/sqrt12

Ex. 3.2 | Q 1.4 | Page 14

Rationalise the denominator of the following

sqrt2/sqrt5

Ex. 3.2 | Q 1.5 | Page 14

Rationalise the denominator of the following

(sqrt3 + 1)/sqrt2

Ex. 3.2 | Q 1.6 | Page 14

Rationalise the denominator of the following

(sqrt2 + sqrt5)/3

Ex. 3.2 | Q 1.7 | Page 14

Rationalise the denominator of the following

(3sqrt2)/sqrt5

Ex. 3.2 | Q 2.1 | Page 14

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

Ex. 3.2 | Q 2.2 | Page 14

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

Ex. 3.2 | Q 2.3 | Page 14

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

Ex. 3.2 | Q 2.4 | Page 14

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



Ex. 3.2 | Q 2.5 | Page 14

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

Ex. 3.2 | Q 2.6 | Page 14

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

Ex. 3.2 | Q 3.1 | Page 14

Express the following with rational denominator:

1/(3 + sqrt2)

Ex. 3.2 | Q 3.2 | Page 14

Express of the following with rational denominator:

1/(sqrt6 - sqrt5)

Ex. 3.2 | Q 3.3 | Page 14

Express the following with rational denominator:

16/(sqrt41 - 5)

Ex. 3.2 | Q 3.4 | Page 14

Express the following with rational denominator:

30/(5sqrt3 - 3sqrt5)

Ex. 3.2 | Q 3.5 | Page 14

Express the following with rational denominator:

1/(2sqrt5 - sqrt3)

Ex. 3.2 | Q 3.6 | Page 14

Express the following with rational denominator:

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

Ex. 3.2 | Q 3.7 | Page 14

Express the following with rational denominator:

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

Ex. 3.2 | Q 3.8 | Page 14

Express the following with rational denominator:

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

Ex. 3.2 | Q 3.9 | Page 14

Express each one of the following with rational denominator:

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

Ex. 3.2 | Q 4.1 | Page 14

Rationales the denominator and simplify:

(3 - sqrt2)/(3 + sqrt2)

Ex. 3.2 | Q 4.2 | Page 14

Rationales the denominator and simplify:

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

Ex. 3.2 | Q 4.3 | Page 14

Rationales the denominator and simplify:

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

Ex. 3.2 | Q 4.4 | Page 14

Rationales the denominator and simplify:

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

Ex. 3.2 | Q 4.5 | Page 14

Rationales the denominator and simplify:

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

Ex. 3.2 | Q 4.6 | Page 14

Rationales the denominator and simplify:

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

Ex. 3.2 | Q 5.1 | Page 14

Simplify:

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

Ex. 3.2 | Q 5.2 | Page 14

Simplify

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

Ex. 3.2 | Q 5.3 | Page 14

Simplify

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

Ex. 3.2 | Q 6.1 | Page 14

In the following determine rational numbers a and b:

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

Ex. 3.2 | Q 6.2 | Page 14

In the following determine rational numbers a and b:

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

Ex. 3.2 | Q 6.3 | Page 14

In the following determine rational numbers a and b:

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

Ex. 3.2 | Q 6.4 | Page 14

In the following determine rational numbers a and b:

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

Ex. 3.2 | Q 6.5 | Page 14

In the following determine rational numbers a and b:

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

Ex. 3.2 | Q 6.6 | Page 14

In the following determine rational numbers a and b:

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

Ex. 3.2 | Q 7 | Page 15

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

Ex. 3.2 | Q 8.1 | Page 15

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)

Ex. 3.2 | Q 8.2 | Page 15

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)

Ex. 3.2 | Q 9.1 | Page 15

Simplify: $\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}$

Ex. 3.2 | Q 9.2 | Page 15

Simplify: $\frac{7 + 3\sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3\sqrt{5}}{3 - \sqrt{5}}$

Ex. 3.2 | Q 10 | Page 15

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

Ex. 3.2 | Q 11 | Page 15

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

Ex. 3.2 | Q 12 | Page 15

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

#### RD Sharma solutions for Mathematics for Class 9 Chapter 3 Rationalisation [Page 16]

Q 1 | Page 16

Write the value of $\left( 2 + \sqrt{3} \right) \left( 2 - \sqrt{3} \right) .$

Q 2 | Page 16

Write the reciprocal of $5 + \sqrt{2}$.

Q 3 | Page 16

Write the rationalisation factor of $7 - 3\sqrt{5}$.

Q 4 | Page 16

If$\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = x + y\sqrt{3},$  find the values of and y.

Q 5 | Page 16

If x= $\sqrt{2} - 1$, then write the value of $\frac{1}{x} .$

Q 6 | Page 16

If $a = \sqrt{2} + 1$,then find the value of  $a - \frac{1}{a}$.

Q 7 | Page 16

If $x = 2 + \sqrt{3}$ ,  find the value of $x + \frac{1}{x}$.

Q 8 | Page 16

Write the rationalisation factor of $\sqrt{5} - 2$.

Q 9 | Page 16

Simplify $\sqrt{3 + 2\sqrt{2}}$.

Q 10 | Page 16

Simplify $\sqrt{3 - 2\sqrt{2}}$.

Q 11 | Page 16

If $x = 3 + 2\sqrt{2}$,then find the value of $\sqrt{x} - \frac{1}{\sqrt{x}}$.

#### RD Sharma solutions for Mathematics for Class 9 Chapter 3 Rationalisation [Pages 16 - 18]

Q 1 | Page 16

$\sqrt{10} \times \sqrt{15}$ is equal to

• 5$\sqrt{6}$

• 6$\sqrt{5}$

• $\sqrt{30}$

• $\sqrt{25}$

Q 2 | Page 16

$\sqrt[5]{6} \times \sqrt[5]{6}$ is equal to

• $\sqrt[5]{36}$

• $\sqrt[5]{6 \times 0}$

• $\sqrt[5]{6}$

• $\sqrt[5]{12}$

Q 3 | Page 16

The rationalisation factor of $\sqrt{3}$ is

• $- \sqrt{3}$

• $\frac{1}{\sqrt{3}}$

• $2\sqrt{3}$

• $- 2\sqrt{3}$

Q 4 | Page 17

The rationalisation factor of $2 + \sqrt{3}$ is

• $2 - \sqrt{3}$

• $2 + \sqrt{3}$

• $\sqrt{2} - 3$

• $\sqrt{3} - 2$

Q 5 | Page 17

If x = $\sqrt{5} + 2$,then $x - \frac{1}{x}$ equals

• $2\sqrt{5}$

• 4

• 2

• $\sqrt{5}$

Q 6 | Page 17

If $\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}$ =$a - b\sqrt{3}$ then

• a = 2, b =1

• a = 2, b =−1

• a = −2, b = 1

• a = b = 1

Q 7 | Page 17

The simplest rationalising factor of  $\sqrt[3]{500}$ is

• $\sqrt[3]{2}$

• $\sqrt[3]{5}$

• $\sqrt{3}$

• none of these

Q 8 | Page 17

The simplest rationalising factor of $\sqrt{3} + \sqrt{5}$ is

• $\sqrt{3} - 5$

• $3 - \sqrt{5}$

• $\sqrt{3} - \sqrt{5}$

• $\sqrt{3} + \sqrt{5}$

Q 9 | Page 17

The simplest rationalising factor of $2\sqrt{5}-$$\sqrt{3}$ is

• $2\sqrt{5} + 3$

• $2\sqrt{5} + \sqrt{3}$

• $\sqrt{5} + \sqrt{3}$

• $\sqrt{5} - \sqrt{3}$

Q 10 | Page 17

If x = $\frac{2}{3 + \sqrt{7}}$,then (x−3)2 =

• 1

• 3

• 6

• 7

Q 11 | Page 17

If $x = 7 + 4\sqrt{3}$ and xy =1, then $\frac{1}{x^2} + \frac{1}{y^2} =$

• 64

• 134

• 194

• 1/49

Q 12 | Page 17

If $x + \sqrt{15} = 4,$ then $x + \frac{1}{x}$ =

• 2

• 4

• 8

• 1

Q 13 | Page 17

If $x = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}$ and $y = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$ then x + y +xy=

• 9

• 5

• 17

• 7

Q 14 | Page 17

If x= $\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}$ and y = $\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}$ , then x2 + y +y2 =

• 101

• 99

• 98

• 102

Q 15 | Page 17

$\frac{1}{\sqrt{9} - \sqrt{8}}$ is equal to

• $3 + 2\sqrt{2}$

• $\frac{1}{3 + 2\sqrt{2}}$

• $3 - 2\sqrt{2}$

• $\frac{3}{2} - \sqrt{2}$

Q 16 | Page 17

The value of $\frac{\sqrt{48} + \sqrt{32}}{\sqrt{27} + \sqrt{18}}$ is

• $\frac{4}{3}$

• 4

• 3

• 3/4`

Q 17 | Page 17

If $\frac{5 - \sqrt{3}}{2 + \sqrt{3}} = x + y\sqrt{3}$ , then

•  x = 13, y = −7

• x = −13, y = 7

• x = −13, y =- 7

• x = 13, y = 7

Q 18 | Page 17

If x = $\sqrt[3]{2 + \sqrt{3}}$ , then $x^3 + \frac{1}{x^3} =$

• 2

• 4

• 8

• 9

Q 19 | Page 17

The value of $\sqrt{3 - 2\sqrt{2}}$ is

• $\sqrt{2} - 1$

• $\sqrt{2} + 1$

• $\sqrt{3} - \sqrt{2}$

• $\sqrt{3} + \sqrt{2}$

Q 20 | Page 18

The value of $\sqrt{5 + 2\sqrt{6}}$ is

• $\sqrt{3} - \sqrt{2}$

• $\sqrt{3} + \sqrt{2}$

• $\sqrt{5} + \sqrt{6}$

• none of these

Q 21 | Page 18

If $\sqrt{2} = 1 . 4142$ then $\sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}}$ is equal to

• 0.1718

•  5.8282

•  0.4142

• 2.4142

Q 22 | Page 18

If $\sqrt{2} = 1 . 414,$ then the value of $\sqrt{6} - \sqrt{3}$ upto three places of decimal is

•  0.235

• 0.707

• 1.414

• 0.471

Q 23 | Page 18

The positive square root of $7 + \sqrt{48}$ is

• $7 + 2\sqrt{3}$

• $7 + \sqrt{3}$

• $\sqrt{3}+2$

• $3 + \sqrt{2}$

Q 24 | Page 18

If $x = \sqrt{6} + \sqrt{5}$,then $x^2 + \frac{1}{x^2} - 2 =$

• $2\sqrt{6}$

• $2\sqrt{5}$

• 24

• 20

Q 25 | Page 18

If $\sqrt{13 - a\sqrt{10}} = \sqrt{8} + \sqrt{5}, \text { then a } =$

• −5

• −6

• −4

• −2

## Chapter 3: Rationalisation

Ex. 3.1Ex. 3.2Others

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

RD Sharma solutions for Mathematics for Class 9 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 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Mathematics for Class 9 chapter 3 Rationalisation are Introduction of Real Number, Concept of 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.

Using RD Sharma Class 9 solutions Rationalisation exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 9 prefer RD Sharma Textbook Solutions to score more in exam.

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