document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248997>Question 248997</A>: <I><SPAN STYLE=\"word-break: break-all;\"> simplify: \r<BR>\n" );
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document.write( "cube root of 144+cube root of 2/3-5 times cube root of 18 \r<BR>\n" );
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document.write( "-Tammam Ahmed  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181454 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=181454\">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=root%283%2C+144%29+%2B+root%283%2C+2%2F3%29+-+5root%283%2C+18%29 ALIGN=MIDDLE  ALT=\"root%283%2C+144%29+%2B+root%283%2C+2%2F3%29+-+5root%283%2C+18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We cannot add or subtract any of these terms because they are not like terms (yet). But we can simplify them. There are two parts to simplifying radicals:<ul><li>Factoring out perfect powers of the root. (In this case we will be factoring out perfect cubes where possible.)</li><li>Rationalizing denominators.</li></ul><BR>\n" );
document.write( "The first cube root has a perfect square factor. The middle cube root needs to be rationalized:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+8%2A18%29+%2B+root%283%2C+%282%2F3%29%289%2F9%29%29+-+5root%283%2C+18%29 ALIGN=MIDDLE  ALT=\"root%283%2C+8%2A18%29+%2B+root%283%2C+%282%2F3%29%289%2F9%29%29+-+5root%283%2C+18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+8%29%2Aroot%283%2C+18%29+%2B+root%283%2C+18%2F27%29+-+5root%283%2C+18%29 ALIGN=MIDDLE  ALT=\"root%283%2C+8%29%2Aroot%283%2C+18%29+%2B+root%283%2C+18%2F27%29+-+5root%283%2C+18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aroot%283%2C+18%29+%2B+root%283%2C+18%29%2Froot%283%2C+27%29+-+5root%283%2C+18%29 ALIGN=MIDDLE  ALT=\"2%2Aroot%283%2C+18%29+%2B+root%283%2C+18%29%2Froot%283%2C+27%29+-+5root%283%2C+18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aroot%283%2C+18%29+%2B+root%283%2C+18%29%2F3+-+5root%283%2C+18%29 ALIGN=MIDDLE  ALT=\"2%2Aroot%283%2C+18%29+%2B+root%283%2C+18%29%2F3+-+5root%283%2C+18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Each cube root is now simplified. And they are now like terms! So we can add and subtract them. Of course we need common denominators first:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Aroot%283%2C+18%29%2F3+%2B+root%283%2C+18%29%2F3+-+15root%283%2C+18%29%2F3 ALIGN=MIDDLE  ALT=\"6%2Aroot%283%2C+18%29%2F3+%2B+root%283%2C+18%29%2F3+-+15root%283%2C+18%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%2Aroot%283%2C+18%29%2F3 ALIGN=MIDDLE  ALT=\"-8%2Aroot%283%2C+18%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-8%29%2F3%29%2Aroot%283%2C+18%29 ALIGN=MIDDLE  ALT=\"%28%28-8%29%2F3%29%2Aroot%283%2C+18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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