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Simplify each of the following expressions :
(i) (3+ √3)(2+ √2) (ii) (3+ √3)(3− √3)
(iii) (5 + √)2 (iv) (√5−√2)(√5+√2)
(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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