document.write( "Question 275432: How would I do this problem? Express 5 over 3-√2 with a rational denominator, in simplest radical form. \n" ); document.write( "
Algebra.Com's Answer #200904 by jsmallt9(3758)\"\" \"About 
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\"5%2F%283-sqrt%282%29%29\"
\n" ); document.write( "Your denominator has two terms. To rationalize a denominator of two terms we take advantage of the pattern: \"%28a%2Bb%29%28a-b%29+=+a%5E2+-+b%5E2\". Every two-term expression (aka binomial) will match one of the two factors on the left side of the pattern. In your case, because you have a \"-\" between the two terms of your denominator, your denominator matches the (a-b) factor in the pattern. If we multiply your denominator by \"3%2Bsqrt%282%29\" we will get, as we can see from the pattern, two perfect squares (with a \"-\" between them). This is exactly what you need to rationalize the denominator.

\n" ); document.write( "Of course we cannot multiply just the denominator by \"3%2Bsqrt%282%29\". We must also multiply the numerator by the same thing. Otherwise we are changing the value of the expression:
\n" ); document.write( "\"%285%2F%283-sqrt%282%29%29%29%28%283%2Bsqrt%282%29%29%2F%283%2Bsqrt%282%29%29%29\"
\n" ); document.write( "On top we use the Distributive Property. On the bottom, the pattern tells us what we will get:
\n" ); document.write( "\"%2815%2B5sqrt%282%29%29%2F%283%5E2-%28sqrt%282%29%29%5E2%29\"
\n" ); document.write( "which simplifies as follows:
\n" ); document.write( "\"%2815%2B5sqrt%282%29%29%2F%289+-+2%29\"
\n" ); document.write( "\"%2815%2B5sqrt%282%29%29%2F7\"
\n" ); document.write( "and the denominator is now rational. \n" ); document.write( "
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