RD Sharma Solutions Class 9 Maths Chapter 3 – Rationalization

RD Sharma Solutions Class 9 Maths Chapter 3 Rationalization: Are looking for some profound guidebooks to start your mathematics exam preparation? Well, we are here with RD Sharma Solutions Class 9 Maths Chapter 3 for you to check out. Not only it is a proven guidebook that helps students with robust Class 9 Maths exam preparation, but also one of the significant options of maths solutions that you can rely upon.

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RD Sharma Solutions Class 9 Maths Chapter 3 

Class 9 Maths RD Sharma Solutions Chapter 3 Rationalization: Exercise-wise Solutions

RD Sharma Solutions Class 9 Chapter 3 Exercise 3.1

RD Sharma Solutions Class 9 Chapter 3 Exercise 3.2

Access answers of RD Sharma Solutions Class 9 Maths Chapter 3

Exercise 3.1

Question 1: Simplify each of the following:

Solution:

(i)

(ii)

Question 2: Simplify the following expressions:

(i) (4 + √7) (3 + √2)

(ii) (3 + √3)(5- √2 )

(iii) (√5 -2)( √3 – √5)

Solution:

(i) (4 + √7) (3 + √2)

= 12 + 4√2 + 3√7 + √14

(ii) (3 + √3)(5- √2 )

= 15 – 3√2 + 5√3 – √6

(iii) (√5 -2)( √3 – √5)

= √15 – √25 – 2√3 + 2√5

= √15 – 5 – 2√3 + 2√5

Question 3: Simplify the following expressions:

(i) (11 + √11) (11 – √11)

(ii) (5 + √7) (5 –√7 )

(iii) (√8 – √2 ) (√8 + √2 )

(iv) (3 + √3) (3 – √3)

(v) (√5 – √2) (√5 + √2)

Solution:

Using Identity: (a – b)(a+b) = a² – b²

(i) (11 + √11) (11 – √11)

= 11² – (√11)²

= 121 – 11

= 110

(ii) (5 + √7) (5 –√7 )

= (5² – (√7)² )

= 25 – 7 = 18

(iii) (√8 – √2 ) (√8 + √2 )

= (√8)² – (√2 ) ²

= 8 -2

= 6

(iv) (3 + √3) (3 – √3)

= (3)² – (√3)²

= 9 – 3

= 6

(v) (√5 – √2) (√5 + √2)

=(√5)² – (√2)²

= 5 – 2

= 3

Question 4: Simplify the following expressions:

(i) (√3 + √7)²

(ii) (√5 – √3)²

(iii) (2√5 + 3√2 )²

Solution:

Using identities: (a – b)² = a² + b² – 2ab and (a + b)² = a² + b² + 2ab

(i) (√3 + √7)²

= (√3)² + (√7)² + 2(√3)( √7)

= 3 + 7 + 2√21

= 10 + 2√21

 

(ii) (√5 – √3)²

= (√5)² + (√3)² – 2(√5)( √3)

= 5 + 3 – 2√15

= 8 – 2√15

(iii) (2√5 + 3√2 )²

= (2√5)² + (3√2 )² + 2(2√5 )( 3√2)

= 20 + 18 + 12√10

= 38 + 12√10

Exercise 3.2

Question 1: Rationalise the denominators of each of the following (i – vii):

(i) 3/ √5 (ii) 3/(2 √5) (iii) 1/ √12 (iv) √2/ √5

(v) (√3 + 1)/ √2 (vi) (√2 + √5)/ √3 (vii) 3 √2/ √5

Solution:

(i) Multiply both the numerator and denominator with the same number to rationalise the denominator.

= 3√5/5

(ii) Multiply both the numerator and denominator with the same number to rationalise the denominator.

(iii) Multiply both the numerator and denominator with the same number to rationalise the denominator.

(iv) Multiply both the numerator and denominator with the same number to rationalise the denominator.

(v) Multiply both the numerator and denominator with the same number to rationalise the denominator.

(vi) Multiply both the numerator and denominator with the same number to rationalise the denominator.

(vii) Multiply both the numerator and denominator with the same number to rationalise the denominator.

Question 2: Find the value to three places of decimals of each of the following. It is given that

√2 = 1.414, √3 = 1.732, √5 = 2.236 and √10 = 3.162

Solution:

Question 3: Express each one of the following with a rational denominator:

Solution:

Using identity: (a + b) (a – b) = a² – b²

(i) Multiply and divide the given number by 3−√2

(ii) Multiply and divide the given number by √6 + √5

(iii) Multiply and divide the given number by √41 + 5

(iv) Multiply and divide the given number by 5√3 + 3√5

(v) Multiply and divide the given number by 2√5 + √3

(vi) Multiply and divide the given number by 2√2 + √3

(vii) Multiply and divide the given number by 6 – 4√2

(viii) Multiply and divide the given number by 2√5 + 3

(ix) Multiply and divide the given number by √(a²+b²) – a

Question 4: Rationales the denominator and simplify:

Solution:

[Use identities: (a + b) (a – b) = a² – b² ; (a + b)² = (a² + 2ab + b² and (a – b)² = (a² – 2ab + b² ]

(i) Multiply both numerator and denominator by √3–√2 to rationalise the denominator.

(ii) Multiply both numerator and denominator by 7–4√3 to rationalise the denominator.

(iii) Multiply both numerator and denominator by 3+2√2 to rationalise the denominator.

(iv) Multiply both numerator and denominator by 3√5+2√6 to rationalise the denominator.

(v) Multiply both numerator and denominator by √48–√18 to rationalise the denominator.

(vi) Multiply both numerator and denominator by 2√2 – 3√3 to rationalise the denominator.

Exercise VSAQs

Question 1: Write the value of (2 + √3) (2 – √3).

Solution:

(2 + √3) (2 – √3)

= (2)² – (√3)²

[Using identity : (a + b)(a – b) = a² – b²]

= 4 – 3

= 1

Question 2: Write the reciprocal of 5 + √2.

Solution:

Question 3: Write the rationalisation factor of 7 – 3√5.

Solution:

The rationalisation factor of 7 – 3√5 is 7 + 3√5

Question 4: If

Find the values of x and y.

Solution:

[Using identities : (a + b)(a – b) = a² – b² and (a – b)² = a² + b² – 2ab]

Question 5: If x = √2 – 1, then write the value of 1/x.

Solution:

x = √2 – 1

or 1/x = 1/(√2 – 1)

Rationalising denominator, we have

= 1/(√2 – 1) x (√2 + 1)/(√2 + 1)

= (√2 + 1)/(2-1)

= √2 + 1

Question 6: Simplify

Solution:

[ Because: (a + b)² = a² + b² + 2ab ]

Question 7: Simplify

Solution:

[ Because: (a – b)² = a² + b² – 2ab ]

Question 8: If a = √2 +1, then find the value of a – 1/a.

Solution:

Given: a = √2 + 1

1/a = 1/(√2 + 1)

= 1/(√2 + 1) x (√2 – 1)/(√2 – 1)

= (√2 – 1)/ ((√2)² – (1)²)

= (√2 – 1)/1

= √2 – 1

Now,

a – 1/a = (√2 + 1) – (√2 – 1)

= 2

Question 9: If x = 2 + √3, find the value of x + 1/x.

Solution:

Given: x = 2 + √3

1/x = 1/(2 + √3)

= 1/(2 + √3) x (2 – √3)/(2 – √3)

= (2 – √3)/ ((2)² – (√3)²)

= (2 – √3)/(4-3)

= (2 – √3)

Now,

x + 1/x = (2 + √3) + (2 – √3)

= 4

Question 10: Write the rationalisation factor of √5 – 2.

Solution:

The rationalisation factor of √5 – 2 is √5 + 2

Question 11: If x = 3 + 2√2, then find the value of √x – 1/√x.

Solution:

Important Topics: RD Sharma Solutions Class 9 Maths Chapter 3

The chapter comprises the three most vital topics that you need to have a look at. These are –

• Rationalization Introduction
• Rationalization of the denominator
• Some important algebraic identities

Well, this is everything that you need to complete your maths syllabus on time. RD Sharma Solutions Class 9 Maths Chapter 3 Rationalization is exactly what you need to study in the 3rd chapter from the class 9 maths syllabus. If you have any doubts regarding the CBSE Class 9 Maths exams, ask in the comments.

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