document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190643>Question 190643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help. I have not done this in ages.<BR>\n" );
document.write( "Write the following expression in simplified radical form.Assume that all variables represent positive real numbers.<BR>\n" );
document.write( "The square root of 48x^3 y^2\r<BR>\n" );
document.write( "\n" );
document.write( "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 #143123 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=143123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2848%2Ax%5E3%2Ay%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2848%2Ax%5E3%2Ay%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%2A3%2Ax%5E3%2Ay%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%2A3%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=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2A3 ALIGN=MIDDLE  ALT=\"16%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%2A3%2Ax%5E2%2Ax%2Ay%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%2A3%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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%29%2Asqrt%283%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%29%2Asqrt%283%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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%283%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%283%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=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%283%29%2Ax%2Asqrt%28x%29%2Asqrt%28y%5E2%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%283%29%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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%283%29%2Ax%2Asqrt%28x%29%2Ay ALIGN=MIDDLE  ALT=\"4%2Asqrt%283%29%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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4xy%2Asqrt%283x%29 ALIGN=MIDDLE  ALT=\"4xy%2Asqrt%283x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange and combine the terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "==================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2848%2Ax%5E3%2Ay%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2848%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=4xy%2Asqrt%283x%29 ALIGN=MIDDLE  ALT=\"4xy%2Asqrt%283x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2848%2Ax%5E3%2Ay%5E2%29=4xy%2Asqrt%283x%29 ALIGN=MIDDLE  ALT=\"sqrt%2848%2Ax%5E3%2Ay%5E2%29=4xy%2Asqrt%283x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is non-negative.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );