Simplifying Surds: Adding and Subtracting

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The discussion focuses on simplifying surds involving addition and subtraction. A user presents a problem with a specific surd expression and seeks guidance on simplification. They successfully simplify \(\sqrt{80}\) to \(2\sqrt{20}\) and combine it with another surd to achieve \(3\sqrt{20}\). The final simplified result is expressed as \(6\sqrt{5}\). The conversation emphasizes the importance of breaking down surds into their simplest forms for easier calculations.
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Ok here is my problem, I am not sure how to simplify surds with additions and subtractions in them such as ones like this:

http://img212.imageshack.us/img212/474/math010iz.gif

At the moment I have managed to simplify it to this:

http://img212.imageshack.us/img212/2011/math026eg.gif

However it is not simplified as possible, can someone give me some words of wisdom? Any help greatly appreciated!
 
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In this case, 80 = 4 x 20, so \sqrt{80}=\sqrt 4 \times\sqrt {20}=2\sqrt {20}.

Therefore \sqrt{20}+\sqrt{80}= (1+2)\sqrt{20}=3\sqrt{20}, which is 3\times 2\times\sqrt 5 = 6\sqrt 5.
 
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