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Prove that each of the following numbers is irrational. (i) 1 + sqrt(2) (ii) 5 + sqrt(2) (iii) 2 + sqrt(5) (iv) 2 - sqrt(3) (v) 5sqrt(2) (vi) (2)/(sqrt(5)) (vii) (1)/(sqrt(3)) (viii) sqrt(2) + sqrt(3) (ix) sqrt(2) + sqrt(5) (x)5 + 3sqrt(2) (xi)2sqrt(3) - 1 (xii) 5 - 2sqrt(3) (xiii) 4 - 5sqrt(2) (xiv) (1)/(sqrt(7))

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