# RD Sharma Solutions Class 9 Maths Chapter 3 Rationalisation Exercise 3.1

RD Sharma Class 9 Mathematics Chapter 3 Exercise 3.1 Rationalisation is provided here. All questions enlisted in Class 9 chapter 3 solutions are solved by BYJUâ€™S experts based on CBSE guidelines. Students can download exercise 3.1 present in the RD Sharma class 9 textbook by clicking on the link below.

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Question 1: Simplify each of the following:

Solution:

(i)

(ii)

Question 2: Simplify the following expressions:

(i) (4 + âˆš7) (3 + âˆš2)

(ii) (3 + âˆš3)(5- âˆš2 )

(iii) (âˆš5 -2)( âˆš3 â€“ âˆš5)

Solution:

(i) (4 + âˆš7) (3 + âˆš2)

= 12 + 4âˆš2 + 3âˆš7 + âˆš14

(ii) (3 + âˆš3)(5- âˆš2 )

= 15 – 3âˆš2 + 5âˆš3 – âˆš6

(iii) (âˆš5 -2)( âˆš3 â€“ âˆš5)

= âˆš15 – âˆš25 – 2âˆš3 + 2âˆš5

= âˆš15 – 5 – 2âˆš3 + 2âˆš5

Question 3: Simplify the following expressions:

(i) (11 + âˆš11) (11 â€“ âˆš11)

(ii) (5 + âˆš7) (5 â€“âˆš7 )

(iii) (âˆš8 â€“ âˆš2 ) (âˆš8 + âˆš2 )

(iv) (3 + âˆš3) (3 – âˆš3)

(v) (âˆš5 – âˆš2) (âˆš5 + âˆš2)

Solution:

Using Identity: (a â€“ b)(a+b) = a2 â€“ b2

(i) (11 + âˆš11) (11 â€“ âˆš11)

= 112 â€“ (âˆš11)2

= 121 â€“ 11

= 110

(ii) (5 + âˆš7) (5 â€“âˆš7 )

= (52 â€“ (âˆš7)2 )

= 25 â€“ 7 = 18

(iii) (âˆš8 â€“ âˆš2 ) (âˆš8 + âˆš2 )

= (âˆš8)2 â€“ (âˆš2 ) 2

= 8 -2

= 6

(iv) (3 + âˆš3) (3 – âˆš3)

= (3)2 â€“ (âˆš3)2

= 9 â€“ 3

= 6

(v) (âˆš5 – âˆš2) (âˆš5 + âˆš2)

=(âˆš5)2 – (âˆš2)2

= 5 â€“ 2

= 3

Question 4: Simplify the following expressions:

(i) (âˆš3 + âˆš7)2

(ii) (âˆš5 â€“ âˆš3)2

(iii) (2âˆš5 + 3âˆš2 )2

Solution:

Using identities: (a â€“ b)2 = a2 + b2 â€“ 2ab and (a + b)2 = a2 + b2 + 2ab

(i) (âˆš3 + âˆš7)2

= (âˆš3)2 + (âˆš7)2 + 2(âˆš3)( âˆš7)

= 3 + 7 + 2âˆš21

= 10 + 2âˆš21

(ii) (âˆš5 â€“ âˆš3)2

= (âˆš5)2 + (âˆš3)2 – 2(âˆš5)( âˆš3)

= 5 + 3 – 2âˆš15

= 8 – 2âˆš15

(iii) (2âˆš5 + 3âˆš2 )2

= (2âˆš5)2 + (3âˆš2 )2 + 2(2âˆš5 )( 3âˆš2)

= 20 + 18 + 12âˆš10

= 38 + 12âˆš10

## RD Sharma Solutions for Class 9 Maths Chapter 3 Rationalisation Exercise 3.1

RD Sharma Solutions Class 9 Maths Chapter 3 Rationalisation Exercise 3.1 is based on Some important Identities as listed below:

• Identity I: (a + b)2 = a2 + 2ab + b2
• Identity II: (a â€“ b)2 = a2 â€“ 2ab + b2
• Identity III: a2 â€“ b2 = (a + b)(a â€“ b)
• Identity IV: (x + a)(x + b) = x2 + (a + b)x + ab