document.write( "Question 1030250: I need help simplifying this expression:
\n" ); document.write( " $\"sqrt%2824%2B8sqrt%285%29%29\"$
\n" ); document.write( "I removed the common factor out of the square root to obtain $\"2sqrt%286%2B2sqrt%285%29%29\"$ , but the answer key says it is $\"2%2B2sqrt%285%29\"$ .
\n" ); document.write( "How is it possible? Am I missing out on a rule here? \n" ); document.write( "

Algebra.Com's Answer #854081 by greenestamps(13326) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Consider this patern:

\n" ); document.write( " $\"%28sqrt%28a%29%2Bsqrt%28b%29%29%5E2=%28a%2Bb%29%2B2sqrt%28ab%29\"$

\n" ); document.write( "Given an expression to be simplified in the form $\"sqrt%28a%2Bb%2Asqrt%28c%29%29\"$ , if you can modify the expression so the coefficient \"b\" on the inside radical is 2, then the expression can be simplified using that pattern.

\n" ); document.write( "In your example, you can take \"4\" out of the coefficient \"8\", leaving the required coefficient \"2\"; the \"4\" goes back inside the radical as $\"sqrt%2816%29\"$ :

\n" ); document.write( " $\"sqrt%2824%2B8sqrt%285%29%29=sqrt%2824%2B2sqrt%2816%2A5%29%29=sqrt%2824%2B2sqrt%2880%29%29\"$

\n" ); document.write( "The pattern now says you want to find integers a and b for which a+b=24 and ab=80. Those integers are 20 and 4, so

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