SOLUTION: Rationalize the denominator: 2____ √[6] - √[5] This one really lost me, can you show the steps???

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: Rationalize the denominator: 2____ √[6] - √[5] This one really lost me, can you show the steps???       Log On

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Question 28478: Rationalize the denominator:
2____
√[6] - √[5]
This one really lost me, can you show the steps???

Answer by Earlsdon(5032) About Me  (Show Source):
You can put this solution on YOUR website!
Rationalise the denominator:
2%2F%28%28sqrt%286%29-sqrt%285%29%29%29 Multiply both the numerator and the denominator by the conjugate of%28sqrt%286%29-sqrt%285%29%29 which is%28sqrt%286%29%2Bsqrt%285%29%29
2%28sqrt%286%29%2Bsqrt%285%29%29%2F%28sqrt%286%29-sqrt%285%29%29%28sqrt%286%29%2Bsqrt%285%29%29 Simplify.
2%28sqrt%286%29%2Bsqrt%285%29%29%2F%286-5%29=2%28sqrt%286%29%2Bsqrt%285%29%29 or 2sqrt%286%29%2B2sqrt%285%29
Explanation:%28a-b%29%28a%2Bb%29+=+a%5E2-b%5E2 In your problem,a+=+sqrt%286%29 and b+=+sqrt%285%29 so a%5E2+=+%28sqrt%286%29%29%5E2 = 6. And b%5E2+=+%28sqrt%285%29%29%5E2 = 5
Multiply sqrt%286%29-sqrt%285%29 by its conjugate sqrt%286%29%2Bsqrt%285%29 using the FOIL method, it works out like this.
%28sqrt%286%29-sqrt%285%29%29%28sqrt%286%29%2Bsqrt%285%29%29+=+6+%2B+%28sqrt%286%29%29%28sqrt%285%29%29+-+%28sqrt%285%29%29%28sqrt%286%29%29+-+5 but, as you can see (I hope), the centre terms drop out leaving you with (6 - 5 = 1)