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

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RD Sharma solutions for Mathematics for Class 9 chapter 3 - Rationalisation - Shaalaa.com
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Solutions for Chapter 3: Rationalisation

Below listed, you can find solutions for Chapter 3 of CBSE RD Sharma for Mathematics for Class 9.


Exercise 3.1Exercise 3.2Exercise 3.3Exercise 3.4
Exercise 3.1 [Pages 2 - 3]

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

Exercise 3.1 | Q 1.1 | Page 2

Simplify of the following:

`root(3)4  xx root(3)16`

Exercise 3.1 | Q 1.2 | Page 2

Simplify of the following:

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

Exercise 3.1 | Q 2.1 | Page 2

Simplify the following expressions:

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

Exercise 3.1 | Q 2.2 | Page 2

Simplify the following expressions:

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

Exercise 3.1 | Q 2.3 | Page 2

Simplify the following expressions:

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

Exercise 3.1 | Q 3.1 | Page 2

Simplify the following expressions:

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

Exercise 3.1 | Q 3.2 | Page 2

Simplify the following expressions:

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

Exercise 3.1 | Q 3.3 | Page 2

Simplify the following expressions:

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

Exercise 3.1 | Q 3.4 | Page 2

Simplify the following expressions:

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

Exercise 3.1 | Q 3.5 | Page 2

Simplify the following expressions:

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

Exercise 3.1 | Q 4.1 | Page 3

Simplify the following expressions:

`(sqrt3 + sqrt7)^2`

Exercise 3.1 | Q 4.2 | Page 3

Simplify the following expressions:

`(sqrt5 - sqrt3)^2`

Exercise 3.1 | Q 4.3 | Page 3

Simplify the following expressions:

`(2sqrt5 + 3sqrt2)^2`

Exercise 3.2 [Pages 14 - 15]

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

Exercise 3.2 | Q 1.1 | Page 14

Rationalise the denominator of each of the following

`3/sqrt5`

Exercise 3.2 | Q 1.2 | Page 14

Rationalise the denominator of the following:

`3/(2sqrt5)`

Exercise 3.2 | Q 1.3 | Page 14

Rationalise the denominator of each of the following 

`1/sqrt12`

Exercise 3.2 | Q 1.4 | Page 14

Rationalise the denominator of the following

`sqrt2/sqrt5`

Exercise 3.2 | Q 1.5 | Page 14

Rationalise the denominator of the following

`(sqrt3 + 1)/sqrt2`

Exercise 3.2 | Q 1.6 | Page 14

Rationalise the denominator of the following

`(sqrt2 + sqrt5)/3`

Exercise 3.2 | Q 1.7 | Page 14

Rationalise the denominator of the following 

`(3sqrt2)/sqrt5`

Exercise 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`

Exercise 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`

Exercise 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`

Exercise 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`

`

Exercise 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`

Exercise 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`

Exercise 3.2 | Q 3.1 | Page 14

Express the following with rational denominator:

`1/(3 + sqrt2)`

Exercise 3.2 | Q 3.2 | Page 14

Express of the following with rational denominator:

`1/(sqrt6 - sqrt5)`

Exercise 3.2 | Q 3.3 | Page 14

Express the following with rational denominator:

`16/(sqrt41 - 5)`

Exercise 3.2 | Q 3.4 | Page 14

Express the following with rational denominator:

`30/(5sqrt3 - 3sqrt5)`

Exercise 3.2 | Q 3.5 | Page 14

Express the following with rational denominator:

`1/(2sqrt5 - sqrt3)`

Exercise 3.2 | Q 3.6 | Page 14

Express the following with rational denominator:

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

Exercise 3.2 | Q 3.7 | Page 14

Express the following with rational denominator:

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

Exercise 3.2 | Q 3.8 | Page 14

Express the following with rational denominator:

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

Exercise 3.2 | Q 3.9 | Page 14

Express each one of the following with rational denominator:

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

Exercise 3.2 | Q 4.1 | Page 14

Rationales the denominator and simplify:

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

Exercise 3.2 | Q 4.2 | Page 14

Rationales the denominator and simplify:

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

Exercise 3.2 | Q 4.3 | Page 14

Rationales the denominator and simplify:

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

Exercise 3.2 | Q 4.4 | Page 14

Rationales the denominator and simplify:

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

Exercise 3.2 | Q 4.5 | Page 14

Rationales the denominator and simplify:

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

Exercise 3.2 | Q 4.6 | Page 14

Rationales the denominator and simplify:

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

Exercise 3.2 | Q 5.1 | Page 14

Simplify:

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

Exercise 3.2 | Q 5.2 | Page 14

Simplify

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

Exercise 3.2 | Q 5.3 | Page 14

Simplify

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

Exercise 3.2 | Q 6.1 | Page 14

In the following determine rational numbers a and b:

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

Exercise 3.2 | Q 6.2 | Page 14

In the following determine rational numbers a and b:

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

Exercise 3.2 | Q 6.3 | Page 14

In the following determine rational numbers a and b:

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

Exercise 3.2 | Q 6.4 | Page 14

In the following determine rational numbers a and b:

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

Exercise 3.2 | Q 6.5 | Page 14

In the following determine rational numbers a and b:

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

Exercise 3.2 | Q 6.6 | Page 14

In the following determine rational numbers a and b:

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

Exercise 3.2 | Q 7 | Page 15

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

Exercise 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)`

Exercise 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)`

Exercise 3.2 | Q 9.1 | Page 15

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

Exercise 3.2 | Q 9.2 | Page 15

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

Exercise 3.2 | Q 10 | Page 15

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

Exercise 3.2 | Q 11 | Page 15

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

Exercise 3.2 | Q 12 | Page 15

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

Exercise 3.3 [Page 16]

RD Sharma solutions for Mathematics for Class 9 Chapter 3 Rationalisation Exercise 3.3 [Page 16]

Exercise 3.3 | Q 1 | Page 16

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

 

Exercise 3.3 | Q 2 | Page 16

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

Exercise 3.3 | Q 3 | Page 16

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

Exercise 3.3 | Q 4 | Page 16

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

Exercise 3.3 | Q 5 | Page 16

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

Exercise 3.3 | Q 6 | Page 16

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

Exercise 3.3 | Q 7 | Page 16

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

Exercise 3.3 | Q 8 | Page 16

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

Exercise 3.3 | Q 9 | Page 16

Simplify \[\sqrt{3 + 2\sqrt{2}}\].

Exercise 3.3 | Q 10 | Page 16

Simplify \[\sqrt{3 - 2\sqrt{2}}\].

Exercise 3.3 | Q 11 | Page 16

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

Exercise 3.4 [Pages 16 - 18]

RD Sharma solutions for Mathematics for Class 9 Chapter 3 Rationalisation Exercise 3.4 [Pages 16 - 18]

Exercise 3.4 | Q 1 | Page 16

\[\sqrt{10} \times \sqrt{15}\] is equal to

  • 5\[\sqrt{6}\]

  • 6\[\sqrt{5}\]

  • \[\sqrt{30}\]

  • \[\sqrt{25}\]

Exercise 3.4 | Q 2 | Page 16

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

  • \[\sqrt[5]{36}\]

  • \[\sqrt[5]{6 \times 0}\]

  • \[\sqrt[5]{6}\]

  • \[\sqrt[5]{12}\]

Exercise 3.4 | Q 3 | Page 16

The rationalisation factor of \[\sqrt{3}\] is 

  • \[- \sqrt{3}\]

  • \[\frac{1}{\sqrt{3}}\]

  • \[2\sqrt{3}\]

  • \[- 2\sqrt{3}\]

Exercise 3.4 | Q 4 | Page 17

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

  • \[2 - \sqrt{3}\]

  • \[2 + \sqrt{3}\]

  • \[\sqrt{2} - 3\]

  • \[\sqrt{3} - 2\]

Exercise 3.4 | Q 5 | Page 17

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

  • \[2\sqrt{5}\]

  • 4

  • 2

  • \[\sqrt{5}\]

Exercise 3.4 | 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

Exercise 3.4 | Q 7 | Page 17

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

  • \[\sqrt[3]{2}\]

  • \[\sqrt[3]{5}\]

  • \[\sqrt{3}\]

  • none of these

Exercise 3.4 | Q 8 | Page 17

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

  • \[\sqrt{3} - 5\]

  • \[3 - \sqrt{5}\]

  • \[\sqrt{3} - \sqrt{5}\]

  • \[\sqrt{3} + \sqrt{5}\]

Exercise 3.4 | Q 9 | Page 17

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

  • \[2\sqrt{5} + 3\]

  • \[2\sqrt{5} + \sqrt{3}\]

  • \[\sqrt{5} + \sqrt{3}\]

  • \[\sqrt{5} - \sqrt{3}\]

Exercise 3.4 | Q 10 | Page 17

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

  • 1

  • 3

  • 6

  • 7

Exercise 3.4 | 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

Exercise 3.4 | Q 12 | Page 17

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

  • 2

  • 4

  • 8

  • 1

Exercise 3.4 | 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

Exercise 3.4 | 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

Exercise 3.4 | Q 15 | Page 17

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

  • \[3 + 2\sqrt{2}\]

  • \[\frac{1}{3 + 2\sqrt{2}}\]

  • \[3 - 2\sqrt{2}\]

  • \[\frac{3}{2} - \sqrt{2}\]

Exercise 3.4 | Q 16 | Page 17

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

  • \[\frac{4}{3}\]

  • 4

  • 3

  • `3/4`

Exercise 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

Exercise 3.4 | Q 18 | Page 17

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

  • 2

  • 4

  • 8

  • 9

Exercise 3.4 | Q 19 | Page 17

The value of \[\sqrt{3 - 2\sqrt{2}}\] is 

  • \[\sqrt{2} - 1\]

  • \[\sqrt{2} + 1\]

  • \[\sqrt{3} - \sqrt{2}\]

  • \[\sqrt{3} + \sqrt{2}\]

Exercise 3.4 | 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

Exercise 3.4 | 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

Exercise 3.4 | 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

Exercise 3.4 | Q 23 | Page 18

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

  • \[7 + 2\sqrt{3}\]

  • \[7 + \sqrt{3}\]

  • \[ \sqrt{3}+2\]

  • \[3 + \sqrt{2}\]

Exercise 3.4 | 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

Exercise 3.4 | Q 25 | Page 18

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

  • −5

  • −6

  • −4

  • −2

Solutions for Chapter 3: Rationalisation

Exercise 3.1Exercise 3.2Exercise 3.3Exercise 3.4
RD Sharma solutions for Mathematics for Class 9 chapter 3 - Rationalisation - Shaalaa.com

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

Shaalaa.com has the CBSE Mathematics Mathematics for Class 9 CBSE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. RD Sharma solutions for Mathematics Mathematics for Class 9 CBSE 3 (Rationalisation) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and provide excellent 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 Mathematics for Class 9 solutions Rationalisation exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in RD Sharma Solutions are essential questions that can be asked in the final exam. Maximum CBSE Mathematics for Class 9 students prefer RD Sharma Textbook Solutions to score more in exams.

Get the free view of Chapter 3, Rationalisation Mathematics for Class 9 additional questions for Mathematics Mathematics for Class 9 CBSE, and you can use Shaalaa.com to keep it handy for your exam preparation.

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