document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132991>Question 132991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify by factoring.  Assume that all expressions under radical represent nonnegative numbers.\r<BR>\n" );
document.write( "\n" );
document.write( "sqrt( 18a^2b )\r<BR>\n" );
document.write( "\n" );
document.write( "I'm confused as I've seen similar problems set up stating to think of them as positive numbers.  Please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97207 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=97207\">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%2818a%5E2b%29 ALIGN=MIDDLE  ALT=\"sqrt%2818a%5E2b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2818%29sqrt%28a%5E2%29sqrt%28b%29 ALIGN=MIDDLE  ALT=\"sqrt%2818%29sqrt%28a%5E2%29sqrt%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the root\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%282%29%2Asqrt%28a%5E2%29sqrt%28b%29%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%282%29%2Asqrt%28a%5E2%29sqrt%28b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2818%29 ALIGN=MIDDLE  ALT=\"sqrt%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%282%29%2Aa%2Asqrt%28b%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%282%29%2Aa%2Asqrt%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2%29\"   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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Aa%2Asqrt%282b%29 ALIGN=MIDDLE  ALT=\"3%2Aa%2Asqrt%282b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the square roots\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2818a%5E2b%29 ALIGN=MIDDLE  ALT=\"sqrt%2818a%5E2b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Aa%2Asqrt%282b%29 ALIGN=MIDDLE  ALT=\"3%2Aa%2Asqrt%282b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2818a%5E2b%29=3%2Aa%2Asqrt%282b%29 ALIGN=MIDDLE  ALT=\"sqrt%2818a%5E2b%29=3%2Aa%2Asqrt%282b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > if a and b are positive numbers (since you cannot take the square root of a negative number)\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );