document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=54715>Question 54715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help with radical 12x^3/5.  \/12x^3/5  The entire equation is under the radical sign. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #36940 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20055)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=36940\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%2812x%5E3%29%2F5%29 ALIGN=MIDDLE  ALT=\"sqrt%28%2812x%5E3%29%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "`<BR>\n" );
document.write( "Break everything into prime factors<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28%282%29%282%29%283%29%28x%29%28x%29%28x%29%29%2F5%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28%282%29%282%29%283%29%28x%29%28x%29%28x%29%29%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "Write (2)·(2) as (2)² and (x)·(x) as (x)²<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28%282%29%5E2%283%29%28x%29%5E2%28x%29%29%2F5%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28%282%29%5E2%283%29%28x%29%5E2%28x%29%29%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "Take the (2)² out in front of the radical as just 2<BR>\n" );
document.write( "Take the (x)² out in front of the radical as just |x|<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2abs%28x%29sqrt%28%28%283%29%28x%29%29%2F5%29 ALIGN=MIDDLE  ALT=\"2abs%28x%29sqrt%28%28%283%29%28x%29%29%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "Rationalize the denominator by multiplying under the<BR>\n" );
document.write( "radical by 5/5:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2abs%28x%29sqrt%28%28%28%283%29%28x%29%29%2F5%29%285%2F5%29%29 ALIGN=MIDDLE  ALT=\"2abs%28x%29sqrt%28%28%28%283%29%28x%29%29%2F5%29%285%2F5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "OR<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2abs%28x%29sqrt%28++%28%2815%29%28x%29%29%2F%28%285%29%285%29%29++%29 ALIGN=MIDDLE  ALT=\"2abs%28x%29sqrt%28++%28%2815%29%28x%29%29%2F%28%285%29%285%29%29++%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "Write the (5)·(5) as (5)²<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2abs%28x%29sqrt%28++%28%2815%29%28x%29%29%2F%28%285%29%5E2%29++%29 ALIGN=MIDDLE  ALT=\"2abs%28x%29sqrt%28++%28%2815%29%28x%29%29%2F%28%285%29%5E2%29++%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "Take (5)² out in front of the radical as 5, and<BR>\n" );
document.write( "since it came from the bottom, put it under the 2|x|.<BR>\n" );
document.write( "The absolute value bars are necessary because the original<BR>\n" );
document.write( "problem is a square root and even root radicals may never<BR>\n" );
document.write( "represent a negative number, so we need absolute<BR>\n" );
document.write( "values around the x in case x turned out to be<BR>\n" );
document.write( "negative.<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282abs%28x%29%2F5%29sqrt%28++%2815%29%28x%29++%29 ALIGN=MIDDLE  ALT=\"%282abs%28x%29%2F5%29sqrt%28++%2815%29%28x%29++%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "This can be written as<BR>\n" );
document.write( "`<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%282abs%28x%29sqrt%28++15x++%29%29%2F5 ALIGN=MIDDLE  ALT=\"++%282abs%28x%29sqrt%28++15x++%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "`<BR>\n" );
document.write( "Edwin </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );