document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176549>Question 176549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how to figure out this problem-- dividing radical expressions<BR>\n" );
document.write( "square root 3x squared y cubed over 4 square root 5xy cubed\r<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 #131635 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=131635\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283x%5E2y%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt%283x%5E2y%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283x%5E2y%5E3%29=xy%2Asqrt%283y%29 ALIGN=MIDDLE  ALT=\"sqrt%283x%5E2y%5E3%29=xy%2Asqrt%283y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is positive.\r<BR>\n" );
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document.write( "Now simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285xy%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt%285xy%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285xy%5E3%29=y%2Asqrt%285xy%29 ALIGN=MIDDLE  ALT=\"sqrt%285xy%5E3%29=y%2Asqrt%285xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is positive.\r<BR>\n" );
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document.write( "So \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283x%5E2y%5E3%29%2F%284%2Asqrt%285xy%5E3%29%29 ALIGN=MIDDLE  ALT=\"sqrt%283x%5E2y%5E3%29%2F%284%2Asqrt%285xy%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "simplifies to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28xy%2Asqrt%283y%29%29%2F%284%2Ay%2Asqrt%285xy%29%29 ALIGN=MIDDLE  ALT=\"%28xy%2Asqrt%283y%29%29%2F%284%2Ay%2Asqrt%285xy%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=%28x%2Ahighlight%28y%29%2Asqrt%283y%29%29%2F%284%2Ahighlight%28y%29%2Asqrt%285xy%29%29 ALIGN=MIDDLE  ALT=\"%28x%2Ahighlight%28y%29%2Asqrt%283y%29%29%2F%284%2Ahighlight%28y%29%2Asqrt%285xy%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Highlight the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Across%28y%29%2Asqrt%283y%29%29%2F%284%2Across%28y%29%2Asqrt%285xy%29%29 ALIGN=MIDDLE  ALT=\"%28x%2Across%28y%29%2Asqrt%283y%29%29%2F%284%2Across%28y%29%2Asqrt%285xy%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Asqrt%283y%29%29%2F%284%2Asqrt%285xy%29%29 ALIGN=MIDDLE  ALT=\"%28x%2Asqrt%283y%29%29%2F%284%2Asqrt%285xy%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Asqrt%283y%29%2Asqrt%285xy%29%29%2F%284%2Asqrt%285xy%29%2Asqrt%285xy%29%29 ALIGN=MIDDLE  ALT=\"%28x%2Asqrt%283y%29%2Asqrt%285xy%29%29%2F%284%2Asqrt%285xy%29%2Asqrt%285xy%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the numerator and denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285xy%29 ALIGN=MIDDLE  ALT=\"sqrt%285xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (to rationalize the denominator)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Asqrt%283y%29%2Asqrt%285xy%29%29%2F%284%2A5xy%29 ALIGN=MIDDLE  ALT=\"%28x%2Asqrt%283y%29%2Asqrt%285xy%29%29%2F%284%2A5xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285xy%29 ALIGN=MIDDLE  ALT=\"sqrt%285xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by itself to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285xy%29%2Asqrt%285xy%29=%28sqrt%285xy%29%29%5E2=5xy ALIGN=MIDDLE  ALT=\"sqrt%285xy%29%2Asqrt%285xy%29=%28sqrt%285xy%29%29%5E2=5xy\"   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=%28x%2Asqrt%283y%2A5xy%29%29%2F%284%2A5xy%29 ALIGN=MIDDLE  ALT=\"%28x%2Asqrt%283y%2A5xy%29%29%2F%284%2A5xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the radicals\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Asqrt%2815xy%5E2%29%29%2F%2820xy%29 ALIGN=MIDDLE  ALT=\"%28x%2Asqrt%2815xy%5E2%29%29%2F%2820xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28x%29%2Asqrt%2815xy%5E2%29%29%2F%2820%2Across%28x%29y%29 ALIGN=MIDDLE  ALT=\"%28cross%28x%29%2Asqrt%2815xy%5E2%29%29%2F%2820%2Across%28x%29y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2815xy%5E2%29%2F%2820y%29 ALIGN=MIDDLE  ALT=\"sqrt%2815xy%5E2%29%2F%2820y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2Asqrt%2815x%29%29%2F%2820y%29 ALIGN=MIDDLE  ALT=\"%28y%2Asqrt%2815x%29%29%2F%2820y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28y%29%2Asqrt%2815x%29%29%2F%2820cross%28y%29%29 ALIGN=MIDDLE  ALT=\"%28cross%28y%29%2Asqrt%2815x%29%29%2F%2820cross%28y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2815x%29%2F20 ALIGN=MIDDLE  ALT=\"sqrt%2815x%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So after all of that, the solution is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283x%5E2y%5E3%29%2F%284%2Asqrt%285xy%5E3%29%29=sqrt%2815x%29%2F20 ALIGN=MIDDLE  ALT=\"sqrt%283x%5E2y%5E3%29%2F%284%2Asqrt%285xy%5E3%29%29=sqrt%2815x%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is positive </SPAN>\n" );
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