document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174247>Question 174247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I don't know how to type this, so I'll try to explain it.<BR>\n" );
document.write( "Square root symbol, with 6 outside (but inside the little section), and inside the square root is another square root symbol. Inside this second square root symbol is a 2. Now subtract from that: square root with 12 inside the little part, and inside the square root is 2 with exponent of 13.\r<BR>\n" );
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document.write( "Hope this makes sense.<BR>\n" );
document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129199 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=129199\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Is the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%286%2Csqrt%282%29%29-root%2812%2C2%5E13%29 ALIGN=MIDDLE  ALT=\"root%286%2Csqrt%282%29%29-root%2812%2C2%5E13%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=root%286%2Csqrt%282%29%29-root%2812%2C2%5E13%29 ALIGN=MIDDLE  ALT=\"root%286%2Csqrt%282%29%29-root%2812%2C2%5E13%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=root%286%2Csqrt%282%29%29-root%2812%2C2%5E%2812%2B1%29%29 ALIGN=MIDDLE  ALT=\"root%286%2Csqrt%282%29%29-root%2812%2C2%5E%2812%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%2813%29 ALIGN=MIDDLE  ALT=\"2%5E%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%2812%2B1%29 ALIGN=MIDDLE  ALT=\"2%5E%2812%2B1%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=root%286%2Csqrt%282%29%29-root%2812%2C2%5E%2812%29%2A2%5E%281%29%29 ALIGN=MIDDLE  ALT=\"root%286%2Csqrt%282%29%29-root%2812%2C2%5E%2812%29%2A2%5E%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the exponent (see note below)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%286%2Csqrt%282%29%29-root%2812%2C2%5E%2812%29%29%2Aroot%2812%2C2%5E%281%29%29%29 ALIGN=MIDDLE  ALT=\"root%286%2Csqrt%282%29%29-root%2812%2C2%5E%2812%29%29%2Aroot%2812%2C2%5E%281%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root (see note below).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%286%2Csqrt%282%29%29-2%2Aroot%2812%2C2%29 ALIGN=MIDDLE  ALT=\"root%286%2Csqrt%282%29%29-2%2Aroot%2812%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the 12th root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E12 ALIGN=MIDDLE  ALT=\"2%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 2 (see note below).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%286%2C2%5E%281%2F2%29%29-2%2Aroot%2812%2C2%29 ALIGN=MIDDLE  ALT=\"root%286%2C2%5E%281%2F2%29%29-2%2Aroot%2812%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Convert from radical notation to exponential notation. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29=2%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29=2%5E%281%2F2%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=%282%5E%281%2F2%29%29%5E%281%2F6%29-2%2Aroot%2812%2C2%29 ALIGN=MIDDLE  ALT=\"%282%5E%281%2F2%29%29%5E%281%2F6%29-2%2Aroot%2812%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Convert from radical notation to exponential notation. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%286%2C2%5E%281%2F2%29%29=%282%5E%281%2F2%29%29%5E%281%2F6%29 ALIGN=MIDDLE  ALT=\"root%286%2C2%5E%281%2F2%29%29=%282%5E%281%2F2%29%29%5E%281%2F6%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=%282%5E%281%2F2%29%29%5E%281%2F6%29-2%2A2%5E%281%2F12%29 ALIGN=MIDDLE  ALT=\"%282%5E%281%2F2%29%29%5E%281%2F6%29-2%2A2%5E%281%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Convert from radical notation to exponential notation. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%2812%2C2%29=2%5E%281%2F12%29 ALIGN=MIDDLE  ALT=\"root%2812%2C2%29=2%5E%281%2F12%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=2%5E%281%2F12%29-2%2A2%5E%281%2F12%29 ALIGN=MIDDLE  ALT=\"2%5E%281%2F12%29-2%2A2%5E%281%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the exponents <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12 ALIGN=MIDDLE  ALT=\"1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take note that the GCF is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%281%2F12%29 ALIGN=MIDDLE  ALT=\"2%5E%281%2F12%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=2%5E%281%2F12%29%281-2%29 ALIGN=MIDDLE  ALT=\"2%5E%281%2F12%29%281-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%281%2F12%29 ALIGN=MIDDLE  ALT=\"2%5E%281%2F12%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=2%5E%281%2F12%29%28-1%29 ALIGN=MIDDLE  ALT=\"2%5E%281%2F12%29%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%2812%2C2%29%28-1%29 ALIGN=MIDDLE  ALT=\"root%2812%2C2%29%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Convert from exponential notation to radical notation. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%281%2F12%29=root%2812%2C2%29 ALIGN=MIDDLE  ALT=\"2%5E%281%2F12%29=root%2812%2C2%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=-root%2812%2C2%29 ALIGN=MIDDLE  ALT=\"-root%2812%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%286%2Csqrt%282%29%29-root%2812%2C2%5E13%29=-root%2812%2C2%29 ALIGN=MIDDLE  ALT=\"root%286%2Csqrt%282%29%29-root%2812%2C2%5E13%29=-root%2812%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Note: the right side reads the negative 12th root of 2)\r<BR>\n" );
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document.write( "Notes:\r<BR>\n" );
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document.write( "I used the following identities to simplify the expression:\r<BR>\n" );
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document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28y%2Bz%29=x%5Ey%2Ax%5Ez ALIGN=MIDDLE  ALT=\"x%5E%28y%2Bz%29=x%5Ey%2Ax%5Ez\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2) <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" );
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document.write( "3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28n%2Cx%5En%29=x ALIGN=MIDDLE  ALT=\"root%28n%2Cx%5En%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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