SOLUTION: Rationalize and simplify (√10- √5)/(√2- √5)

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Question 233254: Rationalize and simplify
(√10- √5)/(√2- √5)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%2810%29-sqrt%285%29%29%2F%28sqrt%282%29-sqrt%285%29%29
Your denominator is a binomial (it has two terms). To rationalize a binomial denominator we need to take advantage of: %28a%2Bb%29%28a-b%29+=+a%5E2+-+b%5E2. On the left we have two binomials, (a+b) and (a-b). Binomials like this are called conjugates. And the pattern says that when conjugates are multiplied we get a binomial made up of perfect square terms!

So with your denominator, sqrt%282%29-sqrt%285%29, we need to multiply by its conjugate, sqrt%282%29%2Bsqrt%285%29, to get a denominator made up of perfect square terms. And, of course, we will have to multiply the numerator by the same thing: