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

## 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

Q 1.1 | Page 13

Rationalise the denominator of each of the following

3/sqrt5

Q 1.2 | Page 13

Rationalise the denominator of each of the following

3/(2sqrt5)

Q 1.3 | Page 13

Rationalise the denominator of each of the following

1/sqrt12

Q 1.4 | Page 13

Rationalise the denominator of the following

sqrt2/sqrt5

Q 1.5 | Page 13

Rationalise the denominator of each of the following

(sqrt3 + 1)/sqrt2

Q 1.6 | Page 13

Rationalise the denominator of the following

(sqrt2 + sqrt5)/3

Q 1.7 | Page 13

Rationalise the denominator of the following

(3sqrt2)/sqrt5

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

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

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

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



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

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

Q 3.1 | Page 14

Express the following with rational denominator:

1/(3 + sqrt2)

Q 3.2 | Page 14

Express of the following with rational denominator:

1/(sqrt6 - sqrt5)

Q 3.3 | Page 14

Express the following with rational denominator:

16/(sqrt41 - 5)

Q 3.4 | Page 14

Express the following with rational denominator:

30/(5sqrt3 - 3sqrt5)

Q 3.5 | Page 14

Express the following with rational denominator:

1/(2sqrt5 - sqrt3)

Q 3.6 | Page 14

Express the following with rational denominator:

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

Q 3.7 | Page 14

Express the following with rational denominator:

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

Q 3.8 | Page 14

Express the following with rational denominator:

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

Q 3.9 | Page 14

Express each one of the following with rational denominator:

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

Q 4.1 | Page 14

Rationales the denominator and simplify:

(3 - sqrt2)/(3 + sqrt2)

Q 4.2 | Page 14

Rationales the denominator and simplify:

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

Q 4.3 | Page 14

Rationales the denominator and simplify:

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

Q 4.5 | Page 14

Rationales the denominator and simplify:

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

Q 4.6 | Page 14

Rationales the denominator and simplify:

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

Q 4.6 | Page 14

Rationales the denominator and simplify:

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

Q 5.1 | Page 14

Simplify:

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

Q 5.2 | Page 14

Simplify

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

Q 5.3 | Page 14

Simplify

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

Q 6.1 | Page 14

In the following determine rational numbers a and b:

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

Q 6.2 | Page 14

In the following determine rational numbers a and b:

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

Q 6.3 | Page 14

In the following determine rational numbers a and b:

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

Q 6.4 | Page 14

In the following determine rational numbers a and b:

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

Q 6.5 | Page 14

In the following determine rational numbers a and b:

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

Q 6.6 | Page 14

In the following determine rational numbers a and b:

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

Q 7 | Page 15

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

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)

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)

Q 10 | Page 14

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

Q 11 | Page 15

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

Q 12 | Page 15

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

## 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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