# Class 9 RD Sharma Solutions – Chapter 3 Rationalisation- Exercise 3.1

### Question 1: Simplify each of the following:

Solution:

(i)

Using the formula:

Here,

(ii)

Using the formula:

Here,

### (iii) (âˆš5 -2)( âˆš3 â€“ âˆš5)

Solution:

(i) (4 + âˆš7) (3 + âˆš2)

= 12 + 4âˆš2 + 3âˆš7 + âˆš14

(ii) (3 + âˆš3)(5- âˆš2)

= 15 â€“ 3âˆš2 + 5âˆš3 â€“ âˆš6

(iii) (âˆš5 – 2)(âˆš3 â€“ âˆš5)

= âˆš15 â€“ âˆš25 â€“ 2âˆš3 + 2âˆš5

= âˆš15 â€“ 5 â€“ 2âˆš3 + 2âˆš5

### (v) (âˆš5 â€“ 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 â€“ âˆš3)

= (3)2 â€“ (âˆš3)2

= 9 â€“ 3

= 6

(v) (âˆš5 â€“ âˆš2) (âˆš5 + âˆš2)

= (âˆš5)2 â€“ (âˆš2)2

= 5 â€“ 2

= 3

### (iii) (2âˆš5 + 3âˆš2 )2

Solution:

Using identities: (a â€“ b)2 = a2 + b2â€“ 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 â€“ 2(âˆš5)(âˆš3)

= 5 + 3 â€“ 2âˆš15

= 8 â€“ 2âˆš15

(iii) (2âˆš5 + 3âˆš2)2

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

= 20 + 18 + 12âˆš10

= 38 + 12âˆš10

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