Simplify each of the following expressions:
(i) (3 + √3)(2 + √2)
(ii) (3 + √3)(3 - √3)
(iii) (√5 + √2 )2
(iv) (√5 - √2)(√5 + √2)
Simplify each of the following expressions:
(i) (3 + √3)(2 + √2)
(ii) (3 + √3)(3 - √3)
(iii) (√5 + √2 )2
(iv) (√5 - √2)(√5 + √2)
Solution and Explanation
(i) (3 + √3)(2 + √2) = 3(2 + √2) + √3 (2 + √2)
= 6 + 3√2 + 2√3 + √6
(ii) (3 + √3) (3 - √3) = (3)2 - (√3)2
= 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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