document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=375104>Question 375104</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The problem asks me to simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers.\r<BR>\n" );
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document.write( "&#8730;(32a^2 b) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266750 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=266750\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2832%2Aa%5E2%2Ab%29 ALIGN=MIDDLE  ALT=\"sqrt%2832%2Aa%5E2%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%2A2%2Aa%5E2%2Ab%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%2A2%2Aa%5E2%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32 ALIGN=MIDDLE  ALT=\"32\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2A2 ALIGN=MIDDLE  ALT=\"16%2A2\"   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=sqrt%2816%29%2Asqrt%282%29%2Asqrt%28a%5E2%29%2Asqrt%28b%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%29%2Asqrt%282%29%2Asqrt%28a%5E2%29%2Asqrt%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29 ALIGN=MIDDLE  ALT=\"sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29\"   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=4%2Asqrt%282%29%2Asqrt%28a%5E2%29%2Asqrt%28b%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%282%29%2Asqrt%28a%5E2%29%2Asqrt%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   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=4%2Asqrt%282%29%2Aa%2Asqrt%28b%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%282%29%2Aa%2Asqrt%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   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=4a%2Asqrt%282b%29 ALIGN=MIDDLE  ALT=\"4a%2Asqrt%282b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Recombine the roots and rearrange the terms.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2832%2Aa%5E2%2Ab%29 ALIGN=MIDDLE  ALT=\"sqrt%2832%2Aa%5E2%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2Asqrt%282b%29 ALIGN=MIDDLE  ALT=\"4a%2Asqrt%282b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2832%2Aa%5E2%2Ab%29=4a%2Asqrt%282b%29 ALIGN=MIDDLE  ALT=\"sqrt%2832%2Aa%5E2%2Ab%29=4a%2Asqrt%282b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is non-negative.\r<BR>\n" );
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document.write( "Jim </SPAN>\n" );
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