document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189564>Question 189564</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i took a test and scored low , but a question that am not sure about is when my professor asked \" what should I multiply 2/cube 2x square by,to rationalize the denominator? the answer is  cube 4x Why isnt it 8 cube x \r<BR>\n" );
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document.write( "thank and have nice day jay <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142247 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=142247\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One thing to note: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C4x%29=root%283%2C2x%2A2x%29=root%283%2C2x%29root%283%2C2x%29 ALIGN=MIDDLE  ALT=\"root%283%2C4x%29=root%283%2C2x%2A2x%29=root%283%2C2x%29root%283%2C2x%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%2Froot%283%2C2x%29 ALIGN=MIDDLE  ALT=\"2%2Froot%283%2C2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "To rationalize the denominator, we need the denominator to be the cube root of something cubed (so the cube root would cancel out). So we need 3 instances of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%5E3 ALIGN=MIDDLE  ALT=\"%282x%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is why we multiply both the numerator and denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C2x%29root%283%2C2x%29 ALIGN=MIDDLE  ALT=\"root%283%2C2x%29root%283%2C2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (add these to the original root to get 3 roots)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Aroot%283%2C2x%29root%283%2C2x%29%29%2F%28root%283%2C2x%29root%283%2C2x%29root%283%2C2x%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both the numerator and denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C2x%29root%283%2C2x%29 ALIGN=MIDDLE  ALT=\"root%283%2C2x%29root%283%2C2x%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%2Aroot%283%2C2x%2A2x%29%29%2F%28root%283%2C2x%2A2x%2A2x%29%29 ALIGN=MIDDLE  ALT=\"%282%2Aroot%283%2C2x%2A2x%29%29%2F%28root%283%2C2x%2A2x%2A2x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the roots.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Aroot%283%2C%282x%29%5E2%29%29%2F%28root%283%2C%282x%29%5E3%29%29 ALIGN=MIDDLE  ALT=\"%282%2Aroot%283%2C%282x%29%5E2%29%29%2F%28root%283%2C%282x%29%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Condense the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Aroot%283%2C%282x%29%5E2%29%29%2F%282x%29 ALIGN=MIDDLE  ALT=\"%282%2Aroot%283%2C%282x%29%5E2%29%29%2F%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the cube root of the cube in the denominator to cancel out the cube root. The denominator is now rationalized.\r<BR>\n" );
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