document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120455>Question 120455</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0132203138/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> how do you reduce -4+sq.root of 40/-2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88277 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=88277\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Start with the expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4+%2B+sqrt%2840%29%29%2F-2 ALIGN=MIDDLE  ALT=\"%28-4+%2B+sqrt%2840%29%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First lets reduce <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2840%29 ALIGN=MIDDLE  ALT=\"sqrt%2840%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%2840%29 ALIGN=MIDDLE  ALT=\"sqrt%2840%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression<BR>\n" );
document.write( "The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. This way the perfect square will become a rational number.\r<BR>\n" );
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document.write( "So let's list the factors of 40\r<BR>\n" );
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document.write( "Factors:\r<BR>\n" );
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document.write( "1, 2, 4, 5, 8, 10, 20, 40\r<BR>\n" );
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document.write( "Notice how 4 is the largest perfect square, so lets break 40 down into 4*10\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%2A10%29 ALIGN=MIDDLE  ALT=\"sqrt%284%2A10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 40 into 4*10<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29%2Asqrt%2810%29 ALIGN=MIDDLE  ALT=\"sqrt%284%29%2Asqrt%2810%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=2%2Asqrt%2810%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect square 4 to get 2 <BR>\n" );
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document.write( "So the expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2840%29 ALIGN=MIDDLE  ALT=\"sqrt%2840%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplifies to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%2810%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-----------------------------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4+%2B+2%2Asqrt%2810%29%29%2F-2 ALIGN=MIDDLE  ALT=\"%28-4+%2B+2%2Asqrt%2810%29%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (using the technique above)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2F-2+%2B+2%2Asqrt%2810%29%2F-2 ALIGN=MIDDLE  ALT=\"-4%2F-2+%2B+2%2Asqrt%2810%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+%2B+2%2Asqrt%2810%29%2F-2 ALIGN=MIDDLE  ALT=\"2+%2B+2%2Asqrt%2810%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2F-2 ALIGN=MIDDLE  ALT=\"-4%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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=2+%2B+-1%2Asqrt%2810%29 ALIGN=MIDDLE  ALT=\"2+%2B+-1%2Asqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F-2 ALIGN=MIDDLE  ALT=\"2%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   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=2-sqrt%2810%29 ALIGN=MIDDLE  ALT=\"2-sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "So the expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4+%2B+sqrt%2840%29%29%2F-2 ALIGN=MIDDLE  ALT=\"%28-4+%2B+sqrt%2840%29%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplifies to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-sqrt%2810%29 ALIGN=MIDDLE  ALT=\"2-sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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