document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=217793>Question 217793</A>: <I><SPAN STYLE=\"word-break: break-all;\"> simplify this expression:<BR>\n" );
document.write( "2*(cube root of 3)+ 4*(cube root of 24)-(cube root of 81)\r<BR>\n" );
document.write( "\n" );
document.write( "please show steps and explain </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #164166 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=164166\">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=2%2Aroot%283%2C3%29%2B4%2Aroot%283%2C24%29-root%283%2C81%29 ALIGN=MIDDLE  ALT=\"2%2Aroot%283%2C3%29%2B4%2Aroot%283%2C24%29-root%283%2C81%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "First we simplify each cube root. To simplify cube roots, try to find perfect cube factors (other than 1) in the radicand (the number inside the radical).<br><BR>\n" );
document.write( "The first radicand has no perfect cube factors. The second and third radicands, however, do have perfect cube factors: 8 and 27 respectively. We can then rewrite them:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aroot%283%2C3%29%2B4%2Aroot%283%2C8%2A3%29-root%283%2C27%2A3%29 ALIGN=MIDDLE  ALT=\"2%2Aroot%283%2C3%29%2B4%2Aroot%283%2C8%2A3%29-root%283%2C27%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can use the property of roots, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28a%2C+x%2Ay%29+=+root%28a%2C+x%29%2Aroot%28a%2Cy%29 ALIGN=MIDDLE  ALT=\"root%28a%2C+x%2Ay%29+=+root%28a%2C+x%29%2Aroot%28a%2Cy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "to separate the perfect cube factors into their own cube roots:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aroot%283%2C3%29%2B4%2Aroot%283%2C8%29%2Aroot%283%2C3%29-root%283%2C27%29%2Aroot%283%2C3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C8%29+=+2 ALIGN=MIDDLE  ALT=\"root%283%2C8%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+27%29+=+3 ALIGN=MIDDLE  ALT=\"root%283%2C+27%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aroot%283%2C3%29%2B4%2A2%2Aroot%283%2C3%29-3%2Aroot%283%2C3%29 ALIGN=MIDDLE  ALT=\"2%2Aroot%283%2C3%29%2B4%2A2%2Aroot%283%2C3%29-3%2Aroot%283%2C3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying the middle term:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aroot%283%2C3%29%2B8%2Aroot%283%2C3%29-3%2Aroot%283%2C3%29 ALIGN=MIDDLE  ALT=\"2%2Aroot%283%2C3%29%2B8%2Aroot%283%2C3%29-3%2Aroot%283%2C3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we have simplified the individual cube roots. Next we try to simplify the entire expression. Can we add and subtract these terms? Answer: yes. They are like terms. Just like 2x+8x-3x are like terms so are these cube roots. If you have trouble seeing this, try using a variable. Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=root%283%2C3%29 ALIGN=MIDDLE  ALT=\"x=root%283%2C3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Then our equation becomes 2x+8x-3x! (On the other hand, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aroot%283%2C4%29%2B8%2Aroot%283%2C6%29 ALIGN=MIDDLE  ALT=\"2%2Aroot%283%2C4%29%2B8%2Aroot%283%2C6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are not like terms because the radicands are different. And <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aroot%283%2C+5%29+%2B+8%2Aroot%284%2C5%29 ALIGN=MIDDLE  ALT=\"2%2Aroot%283%2C+5%29+%2B+8%2Aroot%284%2C5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are not like terms because they are different roots.)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aroot%283%2C3%29%2B8%2Aroot%283%2C3%29-3%2Aroot%283%2C3%29+=+%282%2B8-3%29%2Aroot%283%2C3%29+=+7%2Aroot%283%2C3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since no more simplifying can be done, we are finished. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );