document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151059>Question 151059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> rationalize the denominator: \r<BR>\n" );
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document.write( "sqrt 2 divided by sqrt 6 - sqrt 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110978 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=110978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282%29%29%2F%28sqrt%286%29-sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%282%29%29%2F%28sqrt%286%29-sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "Take note that the conjugate of the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%29-sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%286%29-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%29%2Bsqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%286%29%2Bsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If we multiply the fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%286%29%2Bsqrt%283%29%29%2F%28sqrt%286%29%2Bsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%286%29%2Bsqrt%283%29%29%2F%28sqrt%286%29%2Bsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this will eliminate the square roots in the denominator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28sqrt%282%29%29%2F%28sqrt%286%29-sqrt%283%29%29%29%28%28sqrt%286%29%2Bsqrt%283%29%29%2F%28sqrt%286%29%2Bsqrt%283%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%286%29%2Bsqrt%283%29%29%2F%28sqrt%286%29%2Bsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%286%29%2Bsqrt%283%29%29%2F%28sqrt%286%29%2Bsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28sqrt%282%29%29%28sqrt%286%29%2Bsqrt%283%29%29%29%2F%28%28sqrt%286%29-sqrt%283%29%29%28sqrt%286%29%2Bsqrt%283%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28sqrt%282%29%29%28sqrt%286%29%2Bsqrt%283%29%29%29%2F%283%29 ALIGN=MIDDLE  ALT=\"%28%28sqrt%282%29%29%28sqrt%286%29%2Bsqrt%283%29%29%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil the denominator to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%286%29-sqrt%283%29%29%28sqrt%286%29%2Bsqrt%283%29%29=sqrt%286%29sqrt%286%29%2Bsqrt%286%29sqrt%283%29-sqrt%283%29sqrt%286%29-sqrt%283%29sqrt%283%29=6-3=3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282%29sqrt%286%29%2Bsqrt%282%29sqrt%283%29%29%2F%283%29 ALIGN=MIDDLE  ALT=\"%28sqrt%282%29sqrt%286%29%2Bsqrt%282%29sqrt%283%29%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2812%29%2Bsqrt%286%29%29%2F%283%29 ALIGN=MIDDLE  ALT=\"%28sqrt%2812%29%2Bsqrt%286%29%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine and multiply the square roots.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Asqrt%283%29%2Bsqrt%286%29%29%2F%283%29 ALIGN=MIDDLE  ALT=\"%282%2Asqrt%283%29%2Bsqrt%286%29%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root.\r<BR>\n" );
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document.write( "So after rationalizing the denominator, the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282%29%29%2F%28sqrt%286%29-sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%282%29%29%2F%28sqrt%286%29-sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Asqrt%283%29%2Bsqrt%286%29%29%2F%283%29 ALIGN=MIDDLE  ALT=\"%282%2Asqrt%283%29%2Bsqrt%286%29%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282%29%29%2F%28sqrt%286%29-sqrt%283%29%29=%282%2Asqrt%283%29%2Bsqrt%286%29%29%2F%283%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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