document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120762>Question 120762</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A very pleasant evening to you Math Solvers! I am encountering some difficulties about radicals, can you please help me. In my problems it is specified that you just need to simplify the following by reducing as much as possible, here it follows:\r<BR>\n" );
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document.write( "->fifth root of 486\r<BR>\n" );
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document.write( "               Thank you very much!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88550 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=88550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start by trying to find all the factors of 486. <BR>\n" );
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document.write( "Since 486 is an even number, obviously 2 is a factor. So you can write that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=486+=+2%2A243 ALIGN=MIDDLE  ALT=\"486+=+2%2A243\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now try to factor 243. A little thought will convince you that 3 is a factor of 243. That<BR>\n" );
document.write( "being the case, you can now say that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=486+=+2%2A3%2A81 ALIGN=MIDDLE  ALT=\"486+=+2%2A3%2A81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that 81 can be factored into 9 times 9. So you now have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=486+=+2%2A3%2A9%2A9 ALIGN=MIDDLE  ALT=\"486+=+2%2A3%2A9%2A9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But each of the 9's can be factored to 3*3 and this further reduces the problem to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=486+=+2%2A3%2A3%2A3%2A3%2A3 ALIGN=MIDDLE  ALT=\"486+=+2%2A3%2A3%2A3%2A3%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and since there are 5 factors of 3, you can further say:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=486+=+2%2A3%5E5 ALIGN=MIDDLE  ALT=\"486+=+2%2A3%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The problem required you to find the 5th root of 486. You can substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A3%5E5 ALIGN=MIDDLE  ALT=\"2%2A3%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > for<BR>\n" );
document.write( "486 and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%285%2C486%29=+root%285%2C2%2A3%5E5%29+=+root%285%2C3%5E5%29%2Aroot%285%2C2%29 ALIGN=MIDDLE  ALT=\"root%285%2C486%29=+root%285%2C2%2A3%5E5%29+=+root%285%2C3%5E5%29%2Aroot%285%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But the 5th root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E5 ALIGN=MIDDLE  ALT=\"3%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 3. Substituting this simplification reduces the problem to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%285%2C486%29+=+3%2Aroot%285%2C2%29 ALIGN=MIDDLE  ALT=\"root%285%2C486%29+=+3%2Aroot%285%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
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