document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83391>Question 83391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> radical 3 divided by radical 12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59891 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=59891\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2Fsqrt%2812%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2Fsqrt%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let's first work on the denominator.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812%29 ALIGN=MIDDLE  ALT=\"sqrt%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%2A3%29 ALIGN=MIDDLE  ALT=\"sqrt%284%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then applying the rule that <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;\" > we can do another conversion to <BR>\n" );
document.write( "see that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812%29+=+sqrt%284%2A3%29+=+sqrt%284%29%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%2812%29+=+sqrt%284%2A3%29+=+sqrt%284%29%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29 ALIGN=MIDDLE  ALT=\"sqrt%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can substitute its equivalent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > so that the next conversion<BR>\n" );
document.write( "in the chain is shown on the right side of the expressions:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812%29+=+sqrt%284%2A3%29+=+sqrt%284%29%2Asqrt%283%29+=+2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%2812%29+=+sqrt%284%2A3%29+=+sqrt%284%29%2Asqrt%283%29+=+2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In the original given expression of the problem, we can now replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812%29 ALIGN=MIDDLE  ALT=\"sqrt%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "by its equivalent form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  That replacement results in the original given<BR>\n" );
document.write( "form of the problem becoming:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2Fsqrt%2812%29+=+sqrt%283%29%2F%282%2Asqrt%283%29%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2Fsqrt%2812%29+=+sqrt%283%29%2F%282%2Asqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > appears in as a factor in both the numerator and the denominator. <BR>\n" );
document.write( "Therefore, it can be canceled and the result becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F%282%2Asqrt%283%29%29+=+cross%28sqrt%283%29%29%2F%282%2Across%28sqrt%283%29%29%29=+1%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the simplified or reduced form of the original expression that was given is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this gets you a little more familiar with radicals and some of the methods you can<BR>\n" );
document.write( "use to simplify expressions involving them.  </SPAN>\n" );
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