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?
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Algebra.Com's Answer #854061 by MathTherapy(10801)\"\" \"About 
You can put this solution on YOUR website!
I need help simplifying this expression:\r\n" );
document.write( "\"sqrt%2824%2B8sqrt%285%29%29\"\r\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\".\r\n" );
document.write( "How is it possible? Am I missing out on a rule here?\r\n" );
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document.write( "This happens to be one of those RARE cases when you can actually factor out a COMMON factor, which happens to be a\r\n" );
document.write( "PERFECT SQUARE (in 4). This is what you did:\r\n" );
document.write( "\"sqrt%2824+%2B+8sqrt%285%29%29\" = \"sqrt%284%286+%2B+2sqrt%285%29%29%29\" \r\n" );
document.write( "                            \"sqrt%284%29+%2A+sqrt%286+%2B+2sqrt%285%29%29\" ----- Applying \"sqrt%28m%2An%29\" = \"sqrt%28m%29sqrt%28n%29\"         \r\n" );
document.write( "                               \"2sqrt%286+%2B+2sqrt%285%29%29\"....At this point, you haven't fully simplified the\r\n" );
document.write( "                                                       expression, and should've continued as follows:  \r\n" );
document.write( "                            \r\n" );
document.write( "                   \"2sqrt%285+%2B+1+%2B+2sqrt%285%2A1%29%29\" ---- Changing 6 to 5 + 1, and 5 to 5*1  \r\n" );
document.write( "                    \"2sqrt%285+%2B+1+%2B+2sqrt%285%29sqrt%281%29%29\" ---- Applying \"sqrt%28m%2An%29\" = \"sqrt%28m%29sqrt%28n%29\"         \r\n" );
document.write( "   \"2sqrt%28%28sqrt%285%29%29%5E2+%2B+%28sqrt%281%29%29%5E2+%2B+2sqrt%285%29sqrt%281%29%29\" --- Converting \r\n" );
document.write( "The above is in the form: \"%28a+%2B+b%29%5E2\", with \"system%28matrix%282%2C3%2C+a%2C+being%2C+sqrt%285%29%2C+b%2C+being%2C+sqrt%281%29%29%29\", and so:\r\n" );
document.write( "\"2sqrt%28%28sqrt%285%29%29%5E2+%2B+%28sqrt%281%29%29%5E2+%2B+2sqrt%285%29sqrt%281%29%29\" then becomes: \"2sqrt%28%28sqrt%285%29+%2B+sqrt%281%29%29%5E2%29\" \r\n" );
document.write( "                                                                                \"2%28sqrt%285%29+%2B+sqrt%281%29%29\" ----- Cancelling SQUARE and SQUARE ROOT\r\n" );
document.write( "                                                                                \"2%28sqrt%285%29+%2B+1%29\" = \"highlight%282sqrt%285%29+%2B+2%29\"\r\n" );
document.write( "                                    This certainly matches the answer key: \"2%2B2sqrt%285%29\"\r\n" );
document.write( "=====\r\n" );
document.write( "On the other hand, this author would've SIMPLIFIED the SURD from the onset, as follows:\r\n" );
document.write( "                                 \"sqrt%2824+%2B+8sqrt%285%29%29\"\r\n" );
document.write( "                       \"sqrt%2824+%2B+2%284%29sqrt%285%29%29\" ----- Replacing 8 with factors, 2 & 4\r\n" );
document.write( "                         \"sqrt%2824+%2B+2sqrt%2816%29sqrt%285%29%29\" ----- Converting 4 to \"sqrt%2816%29\"\r\n" );
document.write( "                              \"sqrt%2824+%2B+2sqrt%2880%29%29\" ----- Applying \"sqrt%28m%29sqrt%28n%29\" = \"sqrt%28mn%29%29\"\r\n" );
document.write( "                        \"sqrt%2824+%2B+2sqrt%2820%2A4%29%29\"                \r\n" );
document.write( "                    \"sqrt%2820+%2B+4+%2B+2sqrt%2820%29sqrt%284%29%29\" ---- Changing 24 to 20 + 4, and applying \"sqrt%28m%2An%29\" = \"sqrt%28m%29sqrt%28n%29\"           \r\n" );
document.write( "  \"sqrt%28%28sqrt%2820%29%29%5E2+%2B+%28sqrt%284%29%29%5E2+%2B+2sqrt%2820%29sqrt%284%29%29\" ---- Converting \r\n" );
document.write( "The above is in the form: \"%28a+%2B+b%29%5E2\", with \"system%28matrix%282%2C3%2C+a%2C+being%2C+sqrt%2820%29%2C+b%2C+being%2C+sqrt%284%29%29%29\", and so:\r\n" );
document.write( "    \"sqrt%28%28sqrt%2820%29%29%5E2+%2B+%28sqrt%284%29%29%5E2+%2B+2sqrt%2820%29sqrt%284%29%29\" then becomes:      \"sqrt%28%28sqrt%2820%29+%2B+sqrt%284%29%29%5E2%29\"\r\n" );
document.write( "                                                                                                 \"sqrt%2820%29+%2B+sqrt%284%29\" ----- Cancelling SQUARE and SQUARE ROOT\r\n" );
document.write( "                                                                                                 \"highlight%282sqrt%285%29+%2B+2%29\"\r\n" );
document.write( "                              This certainly matches the answer key: \"2%2B2sqrt%285%29\"
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