document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201810>Question 201810</A>: <I><SPAN STYLE=\"word-break: break-all;\"> IN response to the answer give for Question 201790 \r<BR>\n" );
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document.write( "This problem is actually cube root form written as sqrt (x)^1/3. The ^1/3 means that each square root has a cube root. If you could please help me again with this problem.\r<BR>\n" );
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document.write( "Cube root sqrt (x) (cube root sqrt (3x^2) - cube root sqrt (81x^2)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152042 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=152042\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> note: you can say \"root(3,x)\" to mean <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Cx%29 ALIGN=MIDDLE  ALT=\"root%283%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Or you can simply say \"the cube root of 2\" to mean <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C2%29 ALIGN=MIDDLE  ALT=\"root%283%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%283%2Cx%29%2A%28root%283%2C3x%5E2%29-root%283%2C81x%5E2%29%29 ALIGN=MIDDLE  ALT=\"root%283%2Cx%29%2A%28root%283%2C3x%5E2%29-root%283%2C81x%5E2%29%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%283%2Cx%29%2Aroot%283%2C3x%5E2%29-root%283%2Cx%29%2Aroot%283%2C81x%5E2%29 ALIGN=MIDDLE  ALT=\"root%283%2Cx%29%2Aroot%283%2C3x%5E2%29-root%283%2Cx%29%2Aroot%283%2C81x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Cx%2A3x%5E2%29-root%283%2Cx%2A81x%5E2%29 ALIGN=MIDDLE  ALT=\"root%283%2Cx%2A3x%5E2%29-root%283%2Cx%2A81x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the roots using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28n%2Cx%29%2Aroot%28n%2Cy%29=root%28n%2Cx%2Ay%29 ALIGN=MIDDLE  ALT=\"root%28n%2Cx%29%2Aroot%28n%2Cy%29=root%28n%2Cx%2Ay%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%283%2C3x%5E3%29-root%283%2C81x%5E3%29 ALIGN=MIDDLE  ALT=\"root%283%2C3x%5E3%29-root%283%2C81x%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C3x%5E3%29-root%283%2C27%2A3x%5E3%29 ALIGN=MIDDLE  ALT=\"root%283%2C3x%5E3%29-root%283%2C27%2A3x%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 81 into 27*3. Note: one factor must be a perfect cube.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C3%29%2Aroot%283%2Cx%5E3%29-root%283%2C27%29%2Aroot%283%2C3%29%2Aroot%283%2Cx%5E3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the roots.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C3%29%2Aroot%283%2Cx%5E3%29-3%2Aroot%283%2C3%29%2Aroot%283%2Cx%5E3%29 ALIGN=MIDDLE  ALT=\"root%283%2C3%29%2Aroot%283%2Cx%5E3%29-3%2Aroot%283%2C3%29%2Aroot%283%2Cx%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the cube root of 27 to get 3.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C3%29%2Ax-3%2Aroot%283%2C3%29%2Ax ALIGN=MIDDLE  ALT=\"root%283%2C3%29%2Ax-3%2Aroot%283%2C3%29%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the cube root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get \"x\".\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Aroot%283%2C3%29-3x%2Aroot%283%2C3%29 ALIGN=MIDDLE  ALT=\"x%2Aroot%283%2C3%29-3x%2Aroot%283%2C3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms and multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3x%29%2Aroot%283%2C3%29 ALIGN=MIDDLE  ALT=\"%28x-3x%29%2Aroot%283%2C3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C3%29 ALIGN=MIDDLE  ALT=\"root%283%2C3%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=-2x%2Aroot%283%2C3%29 ALIGN=MIDDLE  ALT=\"-2x%2Aroot%283%2C3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2Cx%29%2A%28root%283%2C3x%5E2%29-root%283%2C81x%5E2%29%29=-2x%2Aroot%283%2C3%29 ALIGN=MIDDLE  ALT=\"root%283%2Cx%29%2A%28root%283%2C3x%5E2%29-root%283%2C81x%5E2%29%29=-2x%2Aroot%283%2C3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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