I need help simplifying this expression:\r\n" );
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\r\n" );
document.write( "I removed the common factor out of the square root to obtain
, but the answer key says it is
.\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" );
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=
\r\n" );
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----- Applying
=
\r\n" );
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....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" );
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---- Changing 6 to 5 + 1, and 5 to 5*1 \r\n" );
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---- Applying
=
\r\n" );
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--- Converting
\r\n" );
document.write( "The above is in the form:
, with
, and so:\r\n" );
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then becomes:
\r\n" );
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----- Cancelling SQUARE and SQUARE ROOT\r\n" );
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=
\r\n" );
document.write( " This certainly matches the answer key:
\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" );
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\r\n" );
document.write( "
----- Replacing 8 with factors, 2 & 4\r\n" );
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----- Converting 4 to
\r\n" );
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----- Applying
=
\r\n" );
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\r\n" );
document.write( "
---- Changing 24 to 20 + 4, and applying
=
\r\n" );
document.write( "
---- Converting
\r\n" );
document.write( "The above is in the form:
, with
, and so:\r\n" );
document.write( "
then becomes:
\r\n" );
document.write( "
----- Cancelling SQUARE and SQUARE ROOT\r\n" );
document.write( "
\r\n" );
document.write( " This certainly matches the answer key: 
\n" );
document.write( "