document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033443>Question 1033443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rationalize the denominator. Simplify, if possible.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%28sqrt%28+x%5E2y%5E5+%29%29%2F%28sqrt%2828x%5E4y%29%29+ ALIGN=MIDDLE  ALT=\"35%28sqrt%28+x%5E2y%5E5+%29%29%2F%28sqrt%2828x%5E4y%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I know that the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y%5E2%28sqrt%287%29%29%2F2x ALIGN=MIDDLE  ALT=\"5y%5E2%28sqrt%287%29%29%2F2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but I'm looking for an in depth explanation on how to get it.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #648079 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=648079\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The numerator is 35 xy^2 sqrt(y).  Every exponent of 2 under the radical becomes 1, and anything left over stays under the radical.<BR>\n" );
document.write( "The denominator is 2x^2(sqrt 7y), because sqrt (28)=sqrt(4)*sqrt(7)<BR>\n" );
document.write( "This is 35y^2 /2x sqrt (7), because the sqrt (y) cancels<BR>\n" );
document.write( "Multiply top and bottom by sqrt (7) to rationalize<BR>\n" );
document.write( "35 y^2 sqrt(7)/2x*7<BR>\n" );
document.write( "=5y^2 sqrt (7)/2x\r<BR>\n" );
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document.write( "Look at each part of the fraction.  Start with the numbers<BR>\n" );
document.write( "On top there is 35.  On the bottom is the square root of 28, which is square root of 4*square root of 7=2 square root of 7. When there is a square root in the denominator, that has to be multiplied by itself to make it rational (fraction of two integers is a rational number, for example, and square root of 7 cannot be written as the fraction of two integers).  This is 35/2 square root (7).  If you multiply top and bottom by square root of 7, the bottom has square root of 7* square root of 7=7.  That is rational.  The numerator now has 35 square root of 7, which is irrational, but it is in the numerator.  <BR>\n" );
document.write( "35 square root of 7/2*7=(5/2) square root of 7.  That is part of the answer, and you can see it.  If the other parts are not clear, ask further, and I will go through that.<BR>\n" );
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