document.write( "Question 423052: Rationalize the denominator and simplify. All variables represent positive real numbers. square root 11 / square root 33 - square root 5 \n" ); document.write( "
Algebra.Com's Answer #295233 by jsmallt9(3758)\"\" \"About 
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\"sqrt%2811%29%2F%28sqrt%2833%29-sqrt%285%29%29\"
\n" ); document.write( "Rationalizing a two-term denominator takes advantage of the pattern:
\n" ); document.write( "\"%28a%2Bb%29%28a-b%29+=+a%5E2+-+b%5E2\"
\n" ); document.write( "Notice that the left side is a product of two-term expressions, like your denominator. And the result, the right side, is made up of nothing but perfect squares.

\n" ); document.write( "Your denominator has a \"-\" between the two terms. SO it will play the role fo (a-b) with the \"a\" being \"sqrt%2833%29\" and the \"b\" being \"sqrt%285%29\". To get the prefect squares, we need to multiply the (a-b) by (a+b). And if we multiply the denominator by something we must also multiply the numerator by the same thing. So we will multiply the numerator and denominator by (a+b), i.e. \"%28sqrt%2833%29%2Bsqrt%285%29%29\":
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\n" ); document.write( "We use the distributive Property to multiply the numerators. In the denominators we know how it will multiply because of the pattern we're using:
\n" ); document.write( "\"%28sqrt%28363%29%2Bsqrt%2855%29%29%2F%28%28sqrt%2833%29%29%5E2-%28sqrt%285%29%29%5E2%29\"
\n" ); document.write( "which simplifies as follows:
\n" ); document.write( "\"%28sqrt%28121%2A3%29%2Bsqrt%2855%29%29%2F%2833-5%29\"
\n" ); document.write( "\"%28sqrt%28121%29%2Asqrt%283%29%2Bsqrt%2855%29%29%2F28\"
\n" ); document.write( "\"%2811sqrt%283%29%2Bsqrt%2855%29%29%2F28\" \n" ); document.write( "
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