document.write( "Question 171500This question is from textbook
\n" ); document.write( ": I need help simplying radicals by factoring. \n" ); document.write( "

Algebra.Com's Answer #126639 by solver91311(24713) $\"\"$ $\"About$

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Share a problem and someone will try to help you. In general, if you are factoring the expression under a radical, look for factors that are perfect squares.\r
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\n" ); document.write( "\n" ); document.write( "For example, if you are faced with $\"sqrt%28c%29\"$ , but you know that $\"c=a%5E2b\"$ , then you can write $\"sqrt%28c%29=sqrt%28a%5E2b%29=a%2Asqrt%28b%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "For a specific example, simplify $\"sqrt%2812%29\"$ . We know that $\"12=4%2A3\"$ , but since $\"4=2%5E2\"$ , $\"12+=+2%5E2%2A3\"$ , so $\"sqrt%2812%29=sqrt%282%5E2%2A3%29=2%2Asqrt%283%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "For a more complex specific example, consider $\"sqrt%28r%5E2%2As%2B2rs%2Bs%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Factor $\"r%5E2%2As%2B2rs%2Bs\"$ completely: $\"s%28r%2B1%29%28r%2B1%29=s%28r%2B1%29%5E2\"$ . Now we have:\r
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\n" ); document.write( "\n" ); document.write( " $\"sqrt%28r%5E2%2As%2B2rs%2Bs%29=sqrt%28s%28r%2B1%29%5E2%29\"$ which can be written $\"%28r%2B1%29sqrt%28s%29\"$ \n" ); document.write( "

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