document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176405>Question 176405</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify 4&#8730;16x^3y^2 -5y&#8730;4x^3 Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #131510 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=131510\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To simplify this expression, we need to simplify the individual radicals.\r<BR>\n" );
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document.write( "Let's simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816x%5E3y%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2816x%5E3y%5E2%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=sqrt%2816x%5E3y%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2816x%5E3y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816x%5E2%2Ax%2Ay%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2816x%5E2%2Ax%2Ay%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Ax ALIGN=MIDDLE  ALT=\"x%5E2%2Ax\"   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=sqrt%2816%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 16 to get 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax%2Asqrt%28x%29%2Asqrt%28y%5E2%29 ALIGN=MIDDLE  ALT=\"4%2Ax%2Asqrt%28x%29%2Asqrt%28y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=4%2Ax%2Asqrt%28x%29%2Ay ALIGN=MIDDLE  ALT=\"4%2Ax%2Asqrt%28x%29%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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=4xy%2Asqrt%28x%29 ALIGN=MIDDLE  ALT=\"4xy%2Asqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816x%5E3y%5E2%29=4xy%2Asqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%2816x%5E3y%5E2%29=4xy%2Asqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is positive.\r<BR>\n" );
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document.write( "Now let's simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284x%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt%284x%5E3%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=sqrt%284x%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt%284x%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284x%5E2%2Ax%29 ALIGN=MIDDLE  ALT=\"sqrt%284x%5E2%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Ax ALIGN=MIDDLE  ALT=\"x%5E2%2Ax\"   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=sqrt%284%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%284%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%28x%5E2%29%2Asqrt%28x%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%28x%5E2%29%2Asqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 4 to get 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2Asqrt%28x%29 ALIGN=MIDDLE  ALT=\"2x%2Asqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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%284x%5E3%29=2x%2Asqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%284x%5E3%29=2x%2Asqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where \"x\" is positive.\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816x%5E3y%5E2%29=4xy%2Asqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%2816x%5E3y%5E2%29=4xy%2Asqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284x%5E3%29=2x%2Asqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%284x%5E3%29=2x%2Asqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (where every variable is positive), this means that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%2816x%5E3y%5E2%29-5y%2Asqrt%284x%5E3%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%2816x%5E3y%5E2%29-5y%2Asqrt%284x%5E3%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=4%2A%284xy%2Asqrt%28x%29%29-5y%2A%282x%2Asqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"4%2A%284xy%2Asqrt%28x%29%29-5y%2A%282x%2Asqrt%28x%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=16xy%2Asqrt%28x%29-5y%2A%282x%2Asqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"16xy%2Asqrt%28x%29-5y%2A%282x%2Asqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 4 and 4xy to get 16xy\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16xy%2Asqrt%28x%29-10xy%2Asqrt%28x%29 ALIGN=MIDDLE  ALT=\"16xy%2Asqrt%28x%29-10xy%2Asqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 5y and 2x to get 10xy\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29%2A%2816xy-10xy%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29%2A%2816xy-10xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%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=sqrt%28x%29%2A%286xy%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29%2A%286xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6xy%2Asqrt%28x%29 ALIGN=MIDDLE  ALT=\"6xy%2Asqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%2816x%5E3y%5E2%29-5y%2Asqrt%284x%5E3%29=6xy%2Asqrt%28x%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%2816x%5E3y%5E2%29-5y%2Asqrt%284x%5E3%29=6xy%2Asqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is positive. </SPAN>\n" );
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