# Simplify each of the following expressions:(i) (ii) (iii) (iv) (i) (3 + √3) (2 + √2)

= 3 (2 + √2) + √3 (2 + √2)

= 3 × 2 + 3√2 + 2√3 + √2 x √3

= 6 +
3√2 + 2√3 + √6

(ii) (3 + √3) (3 - √3)            [Since, (a + b) (a – b) = a2 – b2]

= 32 – (√3)2

= 9 – 3

= 6

(iii) (√5 + √2)2           [Since, (a + b)2 = a2 + b2 + 2ab]

= (√5)2 + (√2)2 + 2 × √5×√2

= 5 + 2 + 2 × = 7 + 2√10

(iv) (√5 - √2) (√5 + √2) [Since, (a + b) (a – b) = a2 – b2]

= (√5)2 – (√2)2

= 5 – 2

= 3

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