document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118228>Question 118228</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3.  Simplify:<BR>\n" );
document.write( "&#8730;[144x10y12z18]\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86331 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=86331\">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%28144%2Ax%5E10y%5E12z%5E18%29 ALIGN=MIDDLE  ALT=\"sqrt%28144%2Ax%5E10y%5E12z%5E18%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%28144%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E10y%5E12z%5E18 ALIGN=MIDDLE  ALT=\"x%5E10y%5E12z%5E18\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28144%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%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;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect square 144 to get 12<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Ax%2Ax%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az ALIGN=MIDDLE  ALT=\"12%2Ax%2Ax%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect squares <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;\" >, <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2 ALIGN=MIDDLE  ALT=\"z%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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Ax%5E5y%5E6z%5E9 ALIGN=MIDDLE  ALT=\"12%2Ax%5E5y%5E6z%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the common terms \r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28144%2Ax%5E10y%5E12z%5E18%29 ALIGN=MIDDLE  ALT=\"sqrt%28144%2Ax%5E10y%5E12z%5E18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Ax%5E5y%5E6z%5E9 ALIGN=MIDDLE  ALT=\"12%2Ax%5E5y%5E6z%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here's another way to do it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28144%2Ax%5E10y%5E12z%5E18%29 ALIGN=MIDDLE  ALT=\"sqrt%28144%2Ax%5E10y%5E12z%5E18%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=%28144%2Ax%5E10y%5E12z%5E18%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28144%2Ax%5E10y%5E12z%5E18%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the radical expression into an exponential expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28144%5E1%29%2Ax%5E10y%5E12z%5E18%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28%28144%5E1%29%2Ax%5E10y%5E12z%5E18%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite 144 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144%5E1 ALIGN=MIDDLE  ALT=\"144%5E1\"   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=144%5E%281%2A%281%2F2%29%29%2Ax%5E%2810%2A%281%2F2%29%29y%5E%2812%2A%281%2F2%29%29z%5E%2818%2A%281%2F2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute the outer exponent\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144%5E%281%2F2%29%2Ax%5E%2810%2F2%29y%5E%2812%2F2%29z%5E%2818%2F2%29 ALIGN=MIDDLE  ALT=\"144%5E%281%2F2%29%2Ax%5E%2810%2F2%29y%5E%2812%2F2%29z%5E%2818%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the exponents\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144%5E%281%2F2%29%2Ax%5E5y%5E6z%5E9 ALIGN=MIDDLE  ALT=\"144%5E%281%2F2%29%2Ax%5E5y%5E6z%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28144%29%2Ax%5E5y%5E6z%5E9 ALIGN=MIDDLE  ALT=\"sqrt%28144%29%2Ax%5E5y%5E6z%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"144%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28144%29 ALIGN=MIDDLE  ALT=\"sqrt%28144%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=12%2Ax%5E5y%5E6z%5E9 ALIGN=MIDDLE  ALT=\"12%2Ax%5E5y%5E6z%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect square 144 to get 12\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28144%2Ax%5E10y%5E12z%5E18%29 ALIGN=MIDDLE  ALT=\"sqrt%28144%2Ax%5E10y%5E12z%5E18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Ax%5E5y%5E6z%5E9 ALIGN=MIDDLE  ALT=\"12%2Ax%5E5y%5E6z%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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