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Simplify: (i) ((5*sqrt(3) + sqrt(50))*(5 - sqrt(24))) / (sqrt(75) - 5*sqrt(2)) (ii) (3*sqrt(2))/(sqrt(6) + sqrt(3)) - (4*sqrt(3))/(sqrt(6) + sqrt(2)) + (sqrt(6))/(sqrt(3) + sqrt(2))

1. (i) 1; (ii) 0
2. (i) 0; (ii) 1
3. (i) sqrt(2); (ii) sqrt(3)
4. (i) 5; (ii) -1

Correct answer: (i) 1; (ii) 0

Solution

Part (i) simplifies because (5*sqrt(3) + 5*sqrt(2)) is a multiple of (sqrt(75) - 5*sqrt(2))'s structure once you account for sqrt(24) = 2*sqrt(6). Part (ii) telescopes to zero after rationalizing.

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