document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147677>Question 147677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2849%2Ax%5E12%2Ay%5E4%2Az%5E8%29 ALIGN=MIDDLE  ALT=\"sqrt%2849%2Ax%5E12%2Ay%5E4%2Az%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108043 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=108043\">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%2849%2Ax%5E12%2Ay%5E4%2Az%5E8%29 ALIGN=MIDDLE  ALT=\"sqrt%2849%2Ax%5E12%2Ay%5E4%2Az%5E8%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%28%287%29%5E2%2Ax%5E12%2Ay%5E4%2Az%5E8%29 ALIGN=MIDDLE  ALT=\"sqrt%28%287%29%5E2%2Ax%5E12%2Ay%5E4%2Az%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49 ALIGN=MIDDLE  ALT=\"49\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%29%5E2 ALIGN=MIDDLE  ALT=\"%287%29%5E2\"   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%28%287%29%5E2%2A%28x%5E6%29%5E2%2Ay%5E4%2Az%5E8%29 ALIGN=MIDDLE  ALT=\"sqrt%28%287%29%5E2%2A%28x%5E6%29%5E2%2Ay%5E4%2Az%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E12 ALIGN=MIDDLE  ALT=\"x%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E6%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E6%29%5E2\"   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%28%287%29%5E2%2A%28x%5E6%29%5E2%2A%28y%5E2%29%5E2%2Az%5E8%29 ALIGN=MIDDLE  ALT=\"sqrt%28%287%29%5E2%2A%28x%5E6%29%5E2%2A%28y%5E2%29%5E2%2Az%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4 ALIGN=MIDDLE  ALT=\"y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2%29%5E2 ALIGN=MIDDLE  ALT=\"%28y%5E2%29%5E2\"   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%28%287%29%5E2%2A%28x%5E6%29%5E2%2A%28y%5E2%29%5E2%2A%28z%5E4%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%287%29%5E2%2A%28x%5E6%29%5E2%2A%28y%5E2%29%5E2%2A%28z%5E4%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E8 ALIGN=MIDDLE  ALT=\"z%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%5E4%29%5E2 ALIGN=MIDDLE  ALT=\"%28z%5E4%29%5E2\"   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%28%287%29%5E2%29%2Asqrt%28%28x%5E6%29%5E2%29%2Asqrt%28%28y%5E2%29%5E2%29%2Asqrt%28%28z%5E4%29%5E2%29 ALIGN=MIDDLE   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%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%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=7%2Ax%5E6%2Ay%5E2%2Az%5E4 ALIGN=MIDDLE  ALT=\"7%2Ax%5E6%2Ay%5E2%2Az%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate each square root. Notice how the squares and the square roots cancel out and we're left with the terms that are in the parenthesis.\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%2849%2Ax%5E12%2Ay%5E4%2Az%5E8%29 ALIGN=MIDDLE  ALT=\"sqrt%2849%2Ax%5E12%2Ay%5E4%2Az%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Ax%5E6%2Ay%5E2%2Az%5E4 ALIGN=MIDDLE  ALT=\"7%2Ax%5E6%2Ay%5E2%2Az%5E4\"   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%2849%2Ax%5E12%2Ay%5E4%2Az%5E8%29=7%2Ax%5E6%2Ay%5E2%2Az%5E4 ALIGN=MIDDLE  ALT=\"sqrt%2849%2Ax%5E12%2Ay%5E4%2Az%5E8%29=7%2Ax%5E6%2Ay%5E2%2Az%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is positive.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );