document.write( "Question 207713: (2√5-3√2) / (2√5+3√2) ..rationalize the numerator i cant seem to do .. help will be appreciated !! \n" ); document.write( "
Algebra.Com's Answer #157112 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\"%282sqrt%285%29-3sqrt%282%29%29%2F%282sqrt%285%29%2B3sqrt%282%29%29\"
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document.write( "Put parentheses around it like this:\r\n" );
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document.write( "\"%28%282sqrt%285%29-3sqrt%282%29%29%2F%282sqrt%285%29%2B3sqrt%282%29%29%29\"\r\n" );
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document.write( "Form the conjugate of whichever you want to rationalize.\r\n" );
document.write( "In this case the numerator.  The numerator is \"2sqrt%285%29-3sqrt%282%29\",\r\n" );
document.write( "It's conjugate is gotten by changing the sign of the second term.\r\n" );
document.write( "So its conjugate is \"2sqrt%285%29%2B3sqrt%282%29\".\r\n" );
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document.write( "Now you put that over itself, like this and put it in \r\n" );
document.write( "parentheses:\r\n" );
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document.write( "\"%28%282sqrt%285%29%2B3sqrt%282%29%29%2F%282sqrt%285%29%2B3sqrt%282%29%29%29\"\r\n" );
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document.write( "Now you multiply these together:\r\n" );
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document.write( "Now you FOIL out the tops and the bottoms:\r\n" );
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document.write( "The middle two terms on top cancel:\r\n" );
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document.write( "And the two terms add together on the bottom:\r\n" );
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document.write( "\"%284sqrt%2825%29-9sqrt%284%29%29%2F%284sqrt%2825%29%2B12sqrt%2810%29%2B9sqrt%284%29%29\"\r\n" );
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document.write( "Now we know the square roots of 25 and 4 so we get\r\n" );
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document.write( "\"%284%2A5-9%2A2%29%2F%284%2A5%2B12sqrt%2810%29%2B9%2A2%29\"\r\n" );
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document.write( "\"%2820-18%29%2F%2820%2B12sqrt%2810%29%2B18%29\"\r\n" );
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document.write( "\"2%2F%2838%2B12sqrt%2810%29%29\"\r\n" );
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document.write( "Factor 2 out of the bottom:\r\n" );
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document.write( "\"2%2F%282%2819%2B6sqrt%2810%29%29%29\"\r\n" );
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document.write( "Cancel the 2's:\r\n" );
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document.write( "\"cross%282%29%5E1%2F%28cross%282%29%5B1%5D%2819%2B6sqrt%2810%29%29%29\"\r\n" );
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document.write( "\"1%2F%2819%2B6sqrt%2810%29%29\"\r\n" );
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document.write( "Now the numerator is rational, because it doesn't\r\n" );
document.write( "contain any square roots.\r\n" );
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document.write( "Edwin

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