document.write( "Question 83550: Simplify and ractionalize all denominators:
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Algebra.Com's Answer #60081 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Stanbon's solution to your problem is incorrect.\r\n" );
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document.write( "Simplify and ractionalize all denominators:\r\n" );
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document.write( "\"3b%2Asqrt%2827a%5E5b%29+%2B+2a%2Asqrt%283a%5E3b%5E3%29\" \r\n" );
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document.write( "There are no denominators to rationalize, so we just simplify this one\r\n" );
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document.write( "Break up what's under the radicals completely into prime factors:\r\n" );
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document.write( "Break up \"27a%5E5b\" into primes as \"3%2A3%2A3%2Aa%2Aa%2Aa%2Aa%2Aa%2Ab\"\r\n" );
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document.write( "Break up \"3a%5E3b%5E3\" into primes \"3%2Aa%2Aa%2Aa%2Ab%2Ab%2Ab\"\r\n" );
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document.write( "Substitute these under the radicals:\r\n" );
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document.write( "\"3b%2Asqrt%283%2A3%2A3%2Aa%2Aa%2Aa%2Aa%2Aa%2Ab%29\" + \"2a%2Asqrt%283%2Aa%2Aa%2Aa%2Ab%2Ab%2Ab%29\"\r\n" );
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document.write( "Since the index of the root is 2 (square root) we group all\r\n" );
document.write( "like factors by twos (pairs) that we can like this.  We will\r\n" );
document.write( "often have factors left over that would not pair up:\r\n" );
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document.write( "\"3b%2Asqrt%28+%283%2A3%29%2A3%2A%28a%2Aa%29%2A%28a%2Aa%29%2Aa%2Ab+%29\" + \"2a%2Asqrt%28+3%2A%28a%2Aa%29%2Aa%2A%28b%2Ab%29%2Ab+%29+\"\r\n" );
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document.write( "Each pair of like factors can be written as a square\r\n" );
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document.write( "\"3b%28sqrt%28++%283%5E2%29%2A3%2A%28a%5E2%29%2A%28a%5E2%29%2Aa%2Ab++%29++%29\" + \"2a%28sqrt%283%2A%28a%5E2%29%2Aa%2A%28b%5E2%29%2Ab%29%29++\"\r\n" );
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document.write( "Take out each square from under the radical out front of the radical,\r\n" );
document.write( "like this, leaving what didn't pair up under the radical:\r\n" );
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document.write( "\"3b%2A3%2Aa%2Aa%2Asqrt%283%2Aa%2Ab%29\" + \"+2a%2Aa%2Ab%28+sqrt%283%2Aa%2Ab%29+%29++\"\r\n" );
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document.write( "Simplify what's in front of the radicals:\r\n" );
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document.write( "\"9a%5E2b%2Asqrt%283ab%29\" + \"2a%5E2b%2Asqrt%283ab%29\"\r\n" );
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document.write( "Now you can factor out GCF = \"a%5E2b%2Asqrt%283ab%29\"\r\n" );
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document.write( "\"a%5E2b%2Asqrt%283ab%29\"(\"9\" + \"2\")\r\n" );
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document.write( "\"a%5E2b%2Asqrt%283ab%2911\"\r\n" );
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document.write( "\"+11a%5E2b%2Asqrt%283ab%29+\"\r\n" );
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document.write( "Edwin

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