document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=761663>Question 761663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the square root.  Do not assume variables represent positive numbers.\r<BR>\n" );
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document.write( "Square root of 18x^3y^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #463387 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=463387\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2818%2Ax%5E3%2Ay%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2818%2Ax%5E3%2Ay%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%289%2A2%2Ax%5E3%2Ay%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%289%2A2%2Ax%5E3%2Ay%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18 ALIGN=MIDDLE  ALT=\"18\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A2 ALIGN=MIDDLE  ALT=\"9%2A2\"   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%289%2A2%2Ax%5E2%2Ax%2Ay%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%289%2A2%2Ax%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;\" > into <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%289%29%2Asqrt%282%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%289%29%2Asqrt%282%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29 ALIGN=MIDDLE  ALT=\"sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%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=3%2Asqrt%282%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%282%29%2Asqrt%28x%5E2%29%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=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   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=3%2Asqrt%282%29%2Aabs%28x%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%282%29%2Aabs%28x%29%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=abs%28x%29 ALIGN=MIDDLE  ALT=\"abs%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=3%2Asqrt%282%29%2Aabs%28x%29%2Asqrt%28x%29%2Aabs%28y%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%282%29%2Aabs%28x%29%2Asqrt%28x%29%2Aabs%28y%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=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=abs%28y%29 ALIGN=MIDDLE  ALT=\"abs%28y%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=3%2Aabs%28x%29%2Aabs%28y%29%2Asqrt%282x%29 ALIGN=MIDDLE  ALT=\"3%2Aabs%28x%29%2Aabs%28y%29%2Asqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange and multiply the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Aabs%28x%2Ay%29%2Asqrt%282x%29 ALIGN=MIDDLE  ALT=\"3%2Aabs%28x%2Ay%29%2Asqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the absolute values.\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=sqrt%2818%2Ax%5E3%2Ay%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2818%2Ax%5E3%2Ay%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Aabs%28x%2Ay%29%2Asqrt%282x%29 ALIGN=MIDDLE  ALT=\"3%2Aabs%28x%2Ay%29%2Asqrt%282x%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=sqrt%2818%2Ax%5E3%2Ay%5E2%29=3%2Aabs%28x%2Ay%29%2Asqrt%282x%29 ALIGN=MIDDLE  ALT=\"sqrt%2818%2Ax%5E3%2Ay%5E2%29=3%2Aabs%28x%2Ay%29%2Asqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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