document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=259334>Question 259334</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the cubed root of -432 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #191814 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=191814\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -432 is not a perfect cube. So it is impossible to find the cube root of -432 exactly.<br><BR>\n" );
document.write( "But -432 does have perfect cube factors so we can simplify it. 8 is 2 cubed and 8 happens to divide evenly into 432. To get the minus sign out of the way, I am going to factor out -8:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+-432%29+=+root%283%2C+-8%2A54%29 ALIGN=MIDDLE  ALT=\"root%283%2C+-432%29+=+root%283%2C+-8%2A54%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the property of radicals, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29+%2A+root%28a%2C+q%29 ALIGN=MIDDLE  ALT=\"root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29+%2A+root%28a%2C+q%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can separate out the perfect square factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+-432%29+=+root%283%2C+-8%2A54%29+=+root%283%2C+-8%29+%2A+root%283%2C+54%29+=+-2root%283%2C+54%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When you reduce fractions you keep reducing until the fraction cannot be reduced any further. Simplifying radicals is similar. Keep simplifying until you cannot simplify any further. So we look at the remaining radical and look for more perfect cube factors. 8 is not a factor of 54. But 27, which is 3 cubed, is a factor of 54:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+-432%29+=+root%283%2C+-8%2A54%29+=+root%283%2C+-8%29+%2A+root%283%2C+54%29+=+-2root%283%2C+54%29+=+-2root%283%2C+27%2A2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the property of radicals to separate the perfect cube factor again we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+-432%29+=+root%283%2C+-8%2A54%29+=+root%283%2C+-8%29+%2A+root%283%2C+54%29+=+-2root%283%2C+54%29+=+-2root%283%2C+27%2A2%29+=+-2root%283%2C+27%29%2Aroot%283%2C+2%29+=+-2%2A3%2Aroot%283%2C+2%29+=+-6root%283%2C+2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This cannot be simplified any further.<br><BR>\n" );
document.write( "So a simplified expression for the cube root of -432 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6root%283%2C2+%29 ALIGN=MIDDLE  ALT=\"-6root%283%2C2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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