Chapter 1

NCERT
Class 9
Mathematics
Solutions
2. Simplify each of the following expressions :

Question:

Simplify each of the following expressions :

(i) (3+ √3)(2+ √2) (ii) (3+ √3)(3− √3)

(iii) (5 + √)2 (iv) (√5−√2)(√5+√2)

Answer:

(i) (3+ √3)(2+ √2) = 3×2+3 √2+2 √3+ √6

= 6+3 √2+2 √3+ √6

(ii) (3+ √3)(3− √3) = (3)2− (√3)2

[(a + b)(a – b) = a2 – b2]

= 9 – 3

= 6

(iii) (√ 5 + √2)2 = (√5)2+(√2)2+(2)(√5)(√2)

= 5+2+2√10 = 7 + 2√10

(iv) ( √5−√2)( √5+√2) = ( √5)2− ( √2)2 = 5 – 2 = 3

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