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Examine whether the following numbres a...

Examine whether the following numbres are rational or irrational:
(i) `(5-sqrt(5)) (5+sqrt(5))` (ii) `(sqrt(3)+2)^(2)`
(iii) `(2sqrt(13))/(3sqrt(52) - 4sqrt(117))` (iv) `sqrt(8) + 4sqrt(32) - 6sqrt(2)`

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