document.write( "Question 383712: PLEASE HELP ME!!! rationalize the denominator. assume all expressions under radical represent positive numbers. √(16/9xy^2) problem is all under the radical.
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Algebra.Com's Answer #271685 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
\"sqrt%2816%2F%289xy%5E2%29%29\"
\n" ); document.write( "As often happens in Math, there are sever ways to do this. The way I like to do it is:
\n" ); document.write( "1. Make the denominator a perfect square.
\n" ); document.write( "9 is a perfect square and so is \"y%5E2\". Only the x in the denominator is not a perfect square. To make the denominator a perfect square, then, we just have to change x into \"x%5E2\" somehow. This can be done by simply multiplying the numerator and denominator of the fraction by x:
\n" ); document.write( "\"sqrt%28%2816%2F%289xy%5E2%29%29%28x%2Fx%29%29\"
\n" ); document.write( "which gives us:
\n" ); document.write( "\"sqrt%28%2816x%29%2F%289x%5E2y%5E2%29%29\"
\n" ); document.write( "Now we can use a property of radicals, \"root%28a%2C+p%2Fq%29+=+root%28a%2C+p%29%2Froot%28a%2C+q%29\", to separate the numerator and denominator into separate square roots:
\n" ); document.write( "\"sqrt%2816x%29%2Fsqrt%289x%5E2y%5E2%29\"
\n" ); document.write( "The denominator, being the square root of a perfect square, simplifies easily:
\n" ); document.write( "\"sqrt%2816x%29%2F3xy\"
\n" ); document.write( "The numerator has a perfect square factor, 16. So we can simplify that, too.
\n" ); document.write( "Using another property of radicals, \"root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29\", we can separate the factors into their own square roots:
\n" ); document.write( "\"%28sqrt%2816%29sqrt%28x%29%29%2F3xy\"
\n" ); document.write( "And the square root of 16 is 4:
\n" ); document.write( "\"%284sqrt%28x%29%29%2F3xy\"
\n" ); document.write( "This is a simplified expression with a rational denominator. \n" ); document.write( "
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