document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=433233>Question 433233</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the best way to find factors to reduce a radical? Example: cube root of 81. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #300293 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=300293\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Do a prime factorization.\r<BR>\n" );
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document.write( "Start with 2.  81 is odd, so 2 is not a factor.\r<BR>\n" );
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document.write( "Consider 3.  The sum of the digits is divisible by 3, so 3 is a factor.\r<BR>\n" );
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document.write( "81 divided by 3 is 27\r<BR>\n" );
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document.write( "The sum of the digits of 27 is divisible by 3, so 3 is a factor.\r<BR>\n" );
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document.write( "27 divided by 3 is 9.\r<BR>\n" );
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document.write( "9 is divisible by 3\r<BR>\n" );
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document.write( "9 divided by 3 is 3.\r<BR>\n" );
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document.write( "Hence, the prime factorization of 81 is 3 times 3 times 3 times 3 times 3.\r<BR>\n" );
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document.write( "Since you are taking a cube root, group like factors in threes.  You have one group of three 3s.  Take three 3s out of the radical and leave one factor of 3 outside of the radical. One factor of 3 remains under the radical.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \sqrt[3]{81}\ =\ \sqrt[3]{3^3}\ \cdot\ \sqrt[3]{3}\ =\ 3\sqrt[3]{3}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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