document.write( "Question 85158: I do not know how to do this problem, so your help is greatly appreciated!\r
\n" ); document.write( "\n" ); document.write( "4. Perform the indicated operations:
\n" ); document.write( "4√[18] + 2√[32] –√[8]\r
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Algebra.Com's Answer #61358 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
Given:
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\n" ); document.write( "\"4%2Asqrt%2818%29%2B+2%2Asqrt%2832%29-sqrt%288%29\"
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\n" ); document.write( "To simplify expressions such as this think in terms of factoring the quantities under the
\n" ); document.write( "radicals. Especially look for factors that are perfect squares because they can be taken outside
\n" ); document.write( "the radicals.
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\n" ); document.write( "Let's operate on one term at a time beginning with \"sqrt%2818%29\". The 18 can be factored into
\n" ); document.write( "\"9%2A2\" which makes the term become \"sqrt%289%2A2%29\". This in turn can be split into two
\n" ); document.write( "radicals: \"sqrt%289%29%2Asqrt%282%29\". But \"sqrt%289%29+=+3\" so the sequence of simplification
\n" ); document.write( "becomes:
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\n" ); document.write( "\"sqrt%2818%29+=+sqrt%289%2A2%29+=+sqrt%289%29%2Asqrt%282%29+=+3%2Asqrt%282%29\"
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\n" ); document.write( "Then putting the original factor of 4 back in front of the radical, you get:
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\n" ); document.write( "\"4%2Asqrt%2818%29+=+4%2A3%2Asqrt%282%29+=+12%2Asqrt%282%29\"
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\n" ); document.write( "Substitute this simplification for the first term in the original problem and you get:
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\n" ); document.write( "\"12%2Asqrt%282%29%2B+2%2Asqrt%2832%29-sqrt%288%29\"
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\n" ); document.write( "On to the second term in the problem. Use the same method on \"sqrt%2832%29\".
\n" ); document.write( "Factor it
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\n" ); document.write( "\"sqrt%2832%29+=+sqrt%2816%2A2%29+=+sqrt%2816%29%2Asqrt%282%29+=+4%2Asqrt%282%29\"
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\n" ); document.write( "Then from the second term, don't forget the 2 that originally multiplied the radical. So
\n" ); document.write( "the entire term from the original equation becomes \"2%2A4%2Asqrt%282%29+=+8%2Asqrt%282%29\".
\n" ); document.write( "Substitute this into the problem equation that already contains the simplified first term
\n" ); document.write( "and the reduced form is now:
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\n" ); document.write( "\"12%2Asqrt%282%29%2B+8%2Asqrt%282%29-sqrt%288%29\"
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\n" ); document.write( "And now to the last term to be simplified:
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\n" ); document.write( "\"sqrt%288%29+=+sqrt%284%2A2%29+=+sqrt%284%29%2Asqrt%282%29+=+2%2Asqrt%282%29\"
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\n" ); document.write( "This term had no multiplier in the original expression, so substituting it back into the
\n" ); document.write( "version with the two terms already simplified results in:
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\n" ); document.write( "\"12%2Asqrt%282%29%2B+8%2Asqrt%282%29-2%2Asqrt%282%29\"
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\n" ); document.write( "Now notice that all three terms contain \"sqrt%282%29\" as a factor. Factoring it out results
\n" ); document.write( "in the distributed multiplication:
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\n" ); document.write( "\"%2812%2B8-2%29%2Asqrt%282%29\"
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\n" ); document.write( "and the terms in the parentheses combine to give the final answer of:
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\n" ); document.write( "\"18%2Asqrt%282%29\"
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\n" ); document.write( "Hope this helps you to understand a method to follow in simplifying radical expressions
\n" ); document.write( "of this sort. \n" ); document.write( "
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