document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103966>Question 103966</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "      8 / cube root of 16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75642 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=75642\">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=8%2Aroot%283%2C16%29 ALIGN=MIDDLE  ALT=\"8%2Aroot%283%2C16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "The goal of simplifying expressions with third roots is to factor the radicand into a product of two numbers.<BR>\n" );
document.write( "One of these two numbers must be a value in which you can take the third root and still get a rational number. \r<BR>\n" );
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document.write( "So let's list the factors of 16\r<BR>\n" );
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document.write( "Factors:\r<BR>\n" );
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document.write( "1, 2, 4, 8, 16\r<BR>\n" );
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document.write( "Notice how 8 is the largest value in which you can take the third root and still get a rational number, so lets break 16 down into 8*2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Aroot%283%2C8%2A2%29 ALIGN=MIDDLE  ALT=\"8%2Aroot%283%2C8%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 16 into 8*2<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Aroot%283%2C8%29%2Aroot%283%2C2%29 ALIGN=MIDDLE  ALT=\"8%2Aroot%283%2C8%29%2Aroot%283%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the roots using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28n%2Cx%2Ay%29=root%28n%2Cx%29%2Aroot%28n%2Cy%29 ALIGN=MIDDLE  ALT=\"root%28n%2Cx%2Ay%29=root%28n%2Cx%29%2Aroot%28n%2Cy%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=8%2A2%2Aroot%283%2C2%29 ALIGN=MIDDLE  ALT=\"8%2A2%2Aroot%283%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the third root of 8 to get 2 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2Aroot%283%2C2%29 ALIGN=MIDDLE  ALT=\"16%2Aroot%283%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
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