document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83596>Question 83596</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify (be sure to rationalize all denominators) \r<BR>\n" );
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document.write( "10. 3b[SQRT(27a^5b)] + 2a[SQRT(3a^3b^3)] \r<BR>\n" );
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document.write( "Here is how I wrote the steps.\r<BR>\n" );
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document.write( "1. 3b[SQRT(27a^5b)] + 2a[SQRT(3a^3b^3)] <BR>\n" );
document.write( "2. 3b[3a^2SQRT(3ab)] + 2a[a^2b^2SQRT(3ab)]<BR>\n" );
document.write( "3. [9a^2+2a^3b^2][SQRT(3ab)]\r<BR>\n" );
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document.write( "I am told that there is a small error in the second step. I was also told to notice in the second term,I have SQRT(3a^3b^3).If I remove the perfect square roots,I'll remove only ab, not a^2b^2. I thought that I had the correct answer and am wonder what the correct step and answer are. Thank you for any help you have!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60110 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=60110\">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=+3b%28sqrt%2827a%5E5b%29%29+%2B+2a%28sqrt%283a%5E3b%5E3%29%29 ALIGN=MIDDLE  ALT=\"+3b%28sqrt%2827a%5E5b%29%29+%2B+2a%28sqrt%283a%5E3b%5E3%29%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=+3b%28sqrt%289%2A3%2Aa%5E2%2Aa%5E2%2Aa%2Ab%29%29+%2B+2a%28sqrt%283%2Aa%5E2%2Aa%2Ab%5E2%2Ab%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 27 into 9*3, <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;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Aa%5E2%2Aa ALIGN=MIDDLE  ALT=\"a%5E2%2Aa%5E2%2Aa\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3 ALIGN=MIDDLE  ALT=\"a%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Aa ALIGN=MIDDLE  ALT=\"a%5E2%2Aa\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E3 ALIGN=MIDDLE  ALT=\"b%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2Ab ALIGN=MIDDLE  ALT=\"b%5E2%2Ab\"   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=+3b%28sqrt%289%29%2Asqrt%283%29%2Asqrt%28a%5E2%29%2Asqrt%28a%5E2%29%2Asqrt%28a%2Ab%29%29+%2B+2a%28sqrt%283%29%2Asqrt%28a%5E2%29%2Asqrt%28a%29%2Asqrt%28b%5E2%29%2Asqrt%28b%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square roots\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3b%283%2Asqrt%283%29%2Aa%2Aa%2Asqrt%28a%2Ab%29%29+%2B+2a%28sqrt%283%29%2Aa%2Asqrt%28a%29%2Ab%2Asqrt%28b%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of all the perfect squares\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3b%283a%5E2%2Asqrt%283%29%2Asqrt%28a%2Ab%29%29+%2B+2a%28ab%2Asqrt%283%29%2Asqrt%28a%29%2Asqrt%28b%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3b%283a%5E2%2Asqrt%283ab%29%29+%2B+2a%28ab%2Asqrt%283ab%29%29 ALIGN=MIDDLE  ALT=\"+3b%283a%5E2%2Asqrt%283ab%29%29+%2B+2a%28ab%2Asqrt%283ab%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine any left over square roots\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9a%5E2b%2Asqrt%283ab%29+%2B+2a%5E2b%2Asqrt%283ab%29%29 ALIGN=MIDDLE  ALT=\"+9a%5E2b%2Asqrt%283ab%29+%2B+2a%5E2b%2Asqrt%283ab%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%289a%5E2b%2B2a%5E2b%29%2Asqrt%283ab%29%29+ ALIGN=MIDDLE  ALT=\"+%289a%5E2b%2B2a%5E2b%29%2Asqrt%283ab%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+11a%5E2b%2Asqrt%283ab%29+ ALIGN=MIDDLE  ALT=\"+11a%5E2b%2Asqrt%283ab%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add. So this is the simplified expression\r<BR>\n" );
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