Simplify each of the following expressions:
(i) `(3+sqrt(3))(2+sqrt(2))`
(ii) `(3+sqrt(3))(3-sqrt(3))`
(iii) `(sqrt(5)+sqrt(2))^2`
(iv) `(sqrt(5)-sqrt(2))(sqrt(5)+sqrt(2))`

Explanation

(i) `(3+ sqrt3)(2+ sqrt2)`

`3(2+ sqrt2) + sqrt3(2+ sqrt2)`

`= 6 + 3sqrt2 + 2sqrt3 + sqrt6`

(ii) `(3+ sqrt3)(3- sqrt3)`

`=3(3-sqrt 3) + sqrt3(3 - sqrt3)`

`= 9 cancel( - 3sqrt3) + cancel(3sqrt3) - (sqrt 3)^2`

`= 9 - 3 = 6`

(iii) `(sqrt 5 + sqrt 2 )^2`

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