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RD Sharma solutions for Class 9 Mathematics chapter 3 - Rationalisation

Mathematics for Class 9 by R D Sharma (2018-19 Session)

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RD Sharma Mathematics Class 9 by R D Sharma (2018-19 Session)

Mathematics for Class 9 by R D Sharma (2018-19 Session)

Chapter 3: Rationalisation

Ex. 3.10Ex. 3.20Others

Chapter 3: Rationalisation Exercise 3.10 solutions [Pages 2 - 3]

Ex. 3.10 | Q 1.1 | Page 2

Simplify of the following:

`root(3)4  xx root(3)16`

Ex. 3.10 | Q 1.2 | Page 2

Simplify of the following:

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

Ex. 3.10 | Q 2.1 | Page 2

Simplify the following expressions:

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

Ex. 3.10 | Q 2.2 | Page 2

Simplify the following expressions:

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

Ex. 3.10 | Q 2.3 | Page 2

Simplify the following expressions:

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

Ex. 3.10 | Q 3.1 | Page 2

Simplify the following expressions:

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

Ex. 3.10 | Q 3.2 | Page 2

Simplify the following expressions:

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

Ex. 3.10 | Q 3.3 | Page 2

Simplify the following expressions:

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

Ex. 3.10 | Q 3.4 | Page 2

Simplify the following expressions:

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

Ex. 3.10 | Q 3.5 | Page 2

Simplify the following expressions:

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

Ex. 3.10 | Q 4.1 | Page 3

Simplify the following expressions:

`(sqrt3 + sqrt7)^2`

Ex. 3.10 | Q 4.2 | Page 3

Simplify the following expressions:

`(sqrt5 - sqrt3)^2`

Ex. 3.10 | Q 4.3 | Page 3

Simplify the following expressions:

`(2sqrt5 + 3sqrt2)^2`

Chapter 3: Rationalisation Exercise 3.20 solutions [Pages 14 - 15]

Ex. 3.20 | Q 1.1 | Page 14

Rationalise the denominator of each of the following

`3/sqrt5`

Ex. 3.20 | Q 1.2 | Page 14

Rationalise the denominator of the following:

`3/(2sqrt5)`

Ex. 3.20 | Q 1.3 | Page 14

Rationalise the denominator of each of the following 

`1/sqrt12`

Ex. 3.20 | Q 1.4 | Page 14

Rationalise the denominator of the following

`sqrt2/sqrt5`

Ex. 3.20 | Q 1.5 | Page 14

Rationalise the denominator of the following

`(sqrt3 + 1)/sqrt2`

Ex. 3.20 | Q 1.6 | Page 14

Rationalise the denominator of the following

`(sqrt2 + sqrt5)/3`

Ex. 3.20 | Q 1.7 | Page 14

Rationalise the denominator of the following 

`(3sqrt2)/sqrt5`

Ex. 3.20 | 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. 3.20 | 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. 3.20 | 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. 3.20 | 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. 3.20 | 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. 3.20 | 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. 3.20 | Q 3.1 | Page 14

Express the following with rational denominator:

`1/(3 + sqrt2)`

Ex. 3.20 | Q 3.2 | Page 14

Express of the following with rational denominator:

`1/(sqrt6 - sqrt5)`

Ex. 3.20 | Q 3.3 | Page 14

Express the following with rational denominator:

`16/(sqrt41 - 5)`

Ex. 3.20 | Q 3.4 | Page 14

Express the following with rational denominator:

`30/(5sqrt3 - 3sqrt5)`

Ex. 3.20 | Q 3.5 | Page 14

Express the following with rational denominator:

`1/(2sqrt5 - sqrt3)`

Ex. 3.20 | Q 3.6 | Page 14

Express the following with rational denominator:

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

Ex. 3.20 | Q 3.7 | Page 14

Express the following with rational denominator:

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

Ex. 3.20 | Q 3.8 | Page 14

Express the following with rational denominator:

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

Ex. 3.20 | Q 3.9 | Page 14

Express each one of the following with rational denominator:

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

Ex. 3.20 | Q 4.1 | Page 14

Rationales the denominator and simplify:

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

Ex. 3.20 | Q 4.2 | Page 14

Rationales the denominator and simplify:

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

Ex. 3.20 | Q 4.3 | Page 14

Rationales the denominator and simplify:

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

Ex. 3.20 | Q 4.4 | Page 14

Rationales the denominator and simplify:

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

Ex. 3.20 | Q 4.5 | Page 14

Rationales the denominator and simplify:

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

Ex. 3.20 | Q 4.6 | Page 14

Rationales the denominator and simplify:

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

Ex. 3.20 | Q 5.1 | Page 14

Simplify:

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

Ex. 3.20 | Q 5.2 | Page 14

Simplify

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

Ex. 3.20 | Q 5.3 | Page 14

Simplify

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

Ex. 3.20 | Q 6.1 | Page 14

In the following determine rational numbers a and b:

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

Ex. 3.20 | Q 6.2 | Page 14

In the following determine rational numbers a and b:

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

Ex. 3.20 | Q 6.3 | Page 14

In the following determine rational numbers a and b:

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

Ex. 3.20 | Q 6.4 | Page 14

In the following determine rational numbers a and b:

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

Ex. 3.20 | Q 6.5 | Page 14

In the following determine rational numbers a and b:

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

Ex. 3.20 | Q 6.6 | Page 14

In the following determine rational numbers a and b:

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

Ex. 3.20 | Q 7 | Page 15

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

Ex. 3.20 | 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. 3.20 | 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. 3.20 | 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. 3.20 | Q 9.2 | Page 15

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

Ex. 3.20 | Q 10 | Page 15

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

Ex. 3.20 | Q 11 | Page 15

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

Ex. 3.20 | Q 12 | Page 15

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

Chapter 3: Rationalisation solutions [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 \[\sqrt{x} - \frac{1}{\sqrt{x}}\].

Chapter 3: Rationalisation solutions [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. 3.10Ex. 3.20Others

RD Sharma Mathematics Class 9 by R D Sharma (2018-19 Session)

Mathematics for Class 9 by R D Sharma (2018-19 Session)

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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