document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167645>Question 167645</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I keep confusing myself with this problem. worksheet states please simplify each of the following. <BR>\n" );
document.write( "sqrt(3x^6)* sqrt(27x^13)= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123543 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=123543\">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=sqrt%283%2Ax%5E6%29%2A+sqrt%2827%2Ax%5E13%29 ALIGN=MIDDLE  ALT=\"sqrt%283%2Ax%5E6%29%2A+sqrt%2827%2Ax%5E13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ***** equation 1 *****<BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%29%2Asqrt%28b%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%29%2Asqrt%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%2Ab%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%2Ax%5E6%2A27%2Ax%5E13%29 ALIGN=MIDDLE  ALT=\"sqrt%283%2Ax%5E6%2A27%2Ax%5E13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "since a*b*c*d = a*c*b*d, this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%2A27%2Ax%5E6%2Ax%5E13%29 ALIGN=MIDDLE  ALT=\"sqrt%283%2A27%2Ax%5E6%2Ax%5E13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Ea%2Ax%5Eb+=+x%5E%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"x%5Ea%2Ax%5Eb+=+x%5E%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%2A27%2Ax%5E%286%2B13%29%29 ALIGN=MIDDLE  ALT=\"sqrt%283%2A27%2Ax%5E%286%2B13%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "simplifying, this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2881%2Ax%5E19%29 ALIGN=MIDDLE  ALT=\"sqrt%2881%2Ax%5E19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ***** equation 2 *****<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to prove the answer is correct, let x be any number that can be easily handled by your calculator.<BR>\n" );
document.write( "for example:<BR>\n" );
document.write( "let x = 3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "equation 1 becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%2A3%5E6%29%2A+sqrt%2827%2A3%5E13%29 ALIGN=MIDDLE  ALT=\"sqrt%283%2A3%5E6%29%2A+sqrt%2827%2A3%5E13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%2A729%29%2A+sqrt%2827%2A4782969%29 ALIGN=MIDDLE  ALT=\"sqrt%283%2A729%29%2A+sqrt%2827%2A4782969%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282187%29%2A+sqrt%2843046721%29 ALIGN=MIDDLE  ALT=\"sqrt%282187%29%2A+sqrt%2843046721%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "306827.6044.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "equation 2 becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2881%2Ax%5E19%29 ALIGN=MIDDLE  ALT=\"sqrt%2881%2Ax%5E19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2881%2A3%5E19%29 ALIGN=MIDDLE  ALT=\"sqrt%2881%2A3%5E19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2881%2A1162261467%29 ALIGN=MIDDLE  ALT=\"sqrt%2881%2A1162261467%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289.414317883%2A10%5E10%29 ALIGN=MIDDLE  ALT=\"sqrt%289.414317883%2A10%5E10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "306827.6044<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the answers come out the same so equation 1 is equivalent to equation 2.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );