Simplify the following expressions. (i) `(5+sqrt(7))(2+sqrt(5))` (ii) `(5+sqrt(5))(5-sqrt(5))`(iii) `(sqrt(3)+sqrt(7))^2` (iv) `(sqrt(11)-sqrt(7))(sqrt(11)+sqrt(7))`

Explanation

(i) `(5+ sqrt 7)(2 + sqrt5)`

`= 5(2 + sqrt5) + sqrt7(2+ sqrt5) `

`= 10 + 5sqrt5 + 2sqrt7 + sqrt35`

(ii) `(5+sqrt5)(5-sqrt5)`

`= (5)^2 - (sqrt5)^2`

using identity `(a+b)(a-b) = a^2 - b^2`

`=25-5 = 20`

(iii) `(sqrt3 + sqrt7)^2`

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