document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=609671>Question 609671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the following expression.\r<BR>\n" );
document.write( "\n" );
document.write( "square root of -6 and -42. Both numbers are next to each other with the square root sign in front of each number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #383895 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=383895\">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%28-6%29%2Asqrt%28-42%29 ALIGN=MIDDLE  ALT=\"sqrt%28-6%29%2Asqrt%28-42%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When the radicand (the number inside) of a square root is negative, then the number is what is called an imaginary number. When working with imaginary numbers the first thing to do is to rewrite them in terms of \"i\":<BR>\n" );
document.write( "<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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2+=+-1 ALIGN=MIDDLE  ALT=\"i%5E2+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Rewriting your numbers in terms of i. Start by factoring out -1 in each radicand:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%2A6%29%2Asqrt%28-1%2A42%29 ALIGN=MIDDLE  ALT=\"sqrt%28-1%2A6%29%2Asqrt%28-1%2A42%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use a property of radicals, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29 ALIGN=MIDDLE  ALT=\"root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to split the factors into separate square roots:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%29%2Asqrt%286%29%2Asqrt%28-1%29%2Asqrt%2842%29 ALIGN=MIDDLE  ALT=\"sqrt%28-1%29%2Asqrt%286%29%2Asqrt%28-1%29%2Asqrt%2842%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "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 \"i\":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%2Asqrt%286%29%2Ai%2Asqrt%2842%29 ALIGN=MIDDLE  ALT=\"i%2Asqrt%286%29%2Ai%2Asqrt%2842%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now we can proceed with \"normal\" simplification. Using the Commutative and Associative Properties to rearrange the order and the grouping:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28i%2Ai%29%2A%28sqrt%286%29%2Asqrt%2842%29%29 ALIGN=MIDDLE  ALT=\"%28i%2Ai%29%2A%28sqrt%286%29%2Asqrt%2842%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28i%5E2%29%2A%28sqrt%28252%29%29 ALIGN=MIDDLE  ALT=\"%28i%5E2%29%2A%28sqrt%28252%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Replacing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2 ALIGN=MIDDLE  ALT=\"i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with -1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2A%28sqrt%28252%29%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2A%28sqrt%28252%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying the square root:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2A%28sqrt%2836%2A7%29%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2A%28sqrt%2836%2A7%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2A%28sqrt%2836%29%2Asqrt%287%29%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2A%28sqrt%2836%29%2Asqrt%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2A%286%2Asqrt%287%29%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2A%286%2Asqrt%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"-6%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the simplified expression. </SPAN>\n" );
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