SOLUTION: 4 over radical 5 plus radical2

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Question 110630: 4 over radical 5 plus radical2

Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
Not sure if your problem is 4%2Fsqrt%285%29%2Bsqrt%282%29 or 4%2F%28sqrt%285%29%2Bsqrt%282%29%29
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I'm also not sure what you want to do with this expression, but I'll assume that you want to rationalize the denominator.
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Let's try the second expression first. In order to rationalize (get the radicals out of) a denominator that is the sum (or difference) of two radicals, you need to remember the factoring rule for the difference of two squares.
:
a%5E2-b%5E2=%28a%2Bb%29%28a-b%29
:
%28sqrt%285%29%2Bsqrt%282%29%29%28sqrt%285%29-sqrt%282%29%29=%28sqrt%285%29%29%5E2-%28sqrt%282%29%29%5E2=5-2=3
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3 is a nice neat rational denominator, so all we have to do is multiply the expression by 1, in the form of %28sqrt%285%29-sqrt%282%29%29%2F%28sqrt%285%29-sqrt%282%29%29
:
%284%2F%28sqrt%285%29%2Bsqrt%282%29%29%29%28%28sqrt%285%29-sqrt%282%29%29%2F%28sqrt%285%29-sqrt%282%29%29%29
%284%2F3%29%28sqrt%285%29-sqrt%282%29%29
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If the problem is actually the first expression, then you need to multiply the first term by 1 in the form of sqrt%285%29%2Fsqrt%285%29, thus:
:
%284%2Fsqrt%285%29%29%28sqrt%285%29%2Fsqrt%285%29%29%2Bsqrt%282%29
%284sqrt%285%29%2F5%29%2Bsqrt%282%29, then find a common denominator and add:
%284sqrt%285%29%2B5sqrt%282%29%29%2F5
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Hope that helps.