document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93427>Question 93427</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> simplify please help me learn this and show all work.  -sqrt(3) (sqrt (-3)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68007 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=68007\">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%283%29%2Asqrt+%28-3%29 ALIGN=MIDDLE  ALT=\"-sqrt%283%29%2Asqrt+%28-3%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+%28-3%2A3%29 ALIGN=MIDDLE  ALT=\"-sqrt+%28-3%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the roots using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29%2Asqrt%28y%29=sqrt%28x%2Ay%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29%2Asqrt%28y%29=sqrt%28x%2Ay%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=-sqrt+%28-9%29 ALIGN=MIDDLE  ALT=\"-sqrt+%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "Now lets focus on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt+%28-9%29 ALIGN=MIDDLE  ALT=\"sqrt+%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=simplifying_square_roots.solver>Simplifying Square Roots (whole numbers only)</A></TD></TR>\n" );
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document.write( "      <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-9%29 ALIGN=MIDDLE  ALT=\"sqrt%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression <BR>\n" );
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document.write( "      <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%2A9%29 ALIGN=MIDDLE  ALT=\"sqrt%28-1%2A9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out a negative 1<BR>\n" );
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document.write( "      <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%29%2Asqrt%289%29 ALIGN=MIDDLE  ALT=\"sqrt%28-1%29%2Asqrt%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square roots using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "      <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%2Asqrt%289%29 ALIGN=MIDDLE  ALT=\"i%2Asqrt%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" > (remember <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"i=sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "      Now lets simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29 ALIGN=MIDDLE  ALT=\"sqrt%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
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document.write( "  Since 9 is a perfect square, we can take the square root of 9 to get a clean number<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29=3 ALIGN=MIDDLE  ALT=\"sqrt%289%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-9%29 ALIGN=MIDDLE  ALT=\"sqrt%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ai ALIGN=MIDDLE  ALT=\"3%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just reintroduce <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" > back in)</TD></TR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt+%28-9%29=-3i ALIGN=MIDDLE  ALT=\"-sqrt+%28-9%29=-3i\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just reintroduce the negative back in) </SPAN>\n" );
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