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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)

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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)

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(i) (3+√3)(2+√2)

(3+√3)(2+√2 )

Opening the brackets, we get, (3×2)+(3×√2)+(√3×2)+(√3×√2)

= 6+3√2+2√3+√6

(ii) (3+√3)(3-√3 )

(3+√3)(3-√3 ) = 32-(√3)2 = 9-3

= 6

(iii) (√5+√2)2

(√5+√2)= √52+(2×√5×√2)+ √22

= 5+2×√10+2 = 7+2√10

(iv) (√5-√2)(√5+√2)

(√5-√2)(√5+√2) = (√52-√22)

= 5-2 = 3

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