document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=35659>Question 35659</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i have worked on this problem and have several different answerw\r<BR>\n" );
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document.write( "5sqrt96a^12b^8\r<BR>\n" );
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document.write( "i came up with 2a^2b^3 5sqrt24 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #21807 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=21807\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There is NO SUCH THING as a \"5sqrt\" of a quantity.  Do you mean <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%2A+sqrt%2896%29 ALIGN=MIDDLE  ALT=\"5+%2A+sqrt%2896%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or do you mean <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%285%2C96%29+ ALIGN=MIDDLE  ALT=\"root%285%2C96%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This could be your problem.  If indeed you mean <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+%2A+sqrt%2896a%5E12%2Ab%5E8%29 ALIGN=MIDDLE  ALT=\"+5+%2A+sqrt%2896a%5E12%2Ab%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then I can do that for you.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A+sqrt%2816a%5E12%2Ab%5E8%29+%2A+sqrt%286%29 ALIGN=MIDDLE  ALT=\"5%2A+sqrt%2816a%5E12%2Ab%5E8%29+%2A+sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A2a%5E6%2Ab%5E4%2A+sqrt%286%29+ ALIGN=MIDDLE  ALT=\"5%2A2a%5E6%2Ab%5E4%2A+sqrt%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10a%5E6%2Ab%5E4+%2A+sqrt%286%29+ ALIGN=MIDDLE  ALT=\"10a%5E6%2Ab%5E4+%2A+sqrt%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "HOWEVER, I continue to insist that the problem PROBABLY was this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+root%285%2C96a%5E12b%5E8%29+ ALIGN=MIDDLE  ALT=\"+root%285%2C96a%5E12b%5E8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If it is a 5th root problem, then you must find perfect 5th powers that divide into this quantity.  The ONLY perfect 5th power that is small enough to be used in most problems is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E5=32 ALIGN=MIDDLE  ALT=\"2%5E5=32\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  It just happens (a coincidence???) that 32 is a factor of 96 and it divides into 96 exactly 3 times.  Also, when you have powers involved, like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E12 ALIGN=MIDDLE  ALT=\"a%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E8 ALIGN=MIDDLE  ALT=\"b%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you need to find a power that is DIVISIBLE by 5, which would be like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E5 ALIGN=MIDDLE  ALT=\"a%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E10 ALIGN=MIDDLE  ALT=\"a%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E15 ALIGN=MIDDLE  ALT=\"a%5E15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, etc.  Now, sort this out into TWO 5th root radicals, and place all the perfect 5th powers up front in the first radical sign, and place all the leftover factors in the second radical.  In this case, you will have to use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E10 ALIGN=MIDDLE  ALT=\"a%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E5 ALIGN=MIDDLE  ALT=\"b%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the perfect powers of \"a\" and \"b\" respectively.  When you do a 5th root of a quantity that is raised to a power, you DIVIDE exponents.  For example <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%285%2Ca%5E10%29+=+a%5E2 ALIGN=MIDDLE  ALT=\"root%285%2Ca%5E10%29+=+a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%285%2Cb%5E5%29=+b%5E1 ALIGN=MIDDLE  ALT=\"root%285%2Cb%5E5%29=+b%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   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%285%2C96a%5E12b%5E8%29+ ALIGN=MIDDLE  ALT=\"+root%285%2C96a%5E12b%5E8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+root%285%2C32a%5E10b%5E5%29%2A+root%285%2C3a%5E2b%5E3%29+ ALIGN=MIDDLE  ALT=\"+root%285%2C32a%5E10b%5E5%29%2A+root%285%2C3a%5E2b%5E3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "The first radical is a perfect 5th power, so you can actually DO this one.  The second radical, containing all the left-overs, will have to stay in the radical sign.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A%28a%5E2%29%2A+b%2A+root%285%2C3a%5E2b%5E3%29+ ALIGN=MIDDLE  ALT=\"+2%2A%28a%5E2%29%2A+b%2A+root%285%2C3a%5E2b%5E3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If this problem was too deep for you, or if you need additional help, check out my Lesson Plans in algebra.com for Radicals (under Square Roots) at Intermediate or College Algebra level, or see my own website under \"Math in Living Color\" and look for those particular topics at those levels of math.\r<BR>\n" );
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document.write( "R^2 at SCC<BR>\n" );
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