Question

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)

Answer 1

(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