document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=90237>Question 90237</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i AM IN NEED OF SOME HELP WITH THESE PROBLEMS i AM NOT DOING TO WELL AT THEM\r<BR>\n" );
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document.write( "-9-SQUARE 108 OVER 3\r<BR>\n" );
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document.write( "AND 6-SQAURE 20 OVER 2\r<BR>\n" );
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document.write( "tHANKS A MILLION FOR THE HELP </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65486 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=65486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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=%28-9+-+sqrt%28108%29%29%2F3 ALIGN=MIDDLE  ALT=\"%28-9+-+sqrt%28108%29%29%2F3\"   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%28108%29 ALIGN=MIDDLE  ALT=\"sqrt%28108%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%28108%29 ALIGN=MIDDLE  ALT=\"sqrt%28108%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 108\r<BR>\n" );
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document.write( "Factors:\r<BR>\n" );
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document.write( "1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54,\r<BR>\n" );
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document.write( "Notice how 36 is the largest perfect square, so lets break 108 down into 36*3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%2A3%29 ALIGN=MIDDLE  ALT=\"sqrt%2836%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 108 into 36*3<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%29%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%2836%29%2Asqrt%283%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=6%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"6%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect square 36 to get 6 <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%28108%29 ALIGN=MIDDLE  ALT=\"sqrt%28108%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=6%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"6%2Asqrt%283%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=%28-9+-+6%2Asqrt%283%29%29%2F3 ALIGN=MIDDLE  ALT=\"%28-9+-+6%2Asqrt%283%29%29%2F3\"   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=-9%2F3+-+6%2Asqrt%283%29%2F3 ALIGN=MIDDLE  ALT=\"-9%2F3+-+6%2Asqrt%283%29%2F3\"   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=-3+-+6%2Asqrt%283%29%2F3 ALIGN=MIDDLE  ALT=\"-3+-+6%2Asqrt%283%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9%2F3 ALIGN=MIDDLE  ALT=\"-9%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   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=-3+-+2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"-3+-+2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F3 ALIGN=MIDDLE  ALT=\"6%2F3\"   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( "So the expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-9+-+sqrt%28108%29%29%2F3 ALIGN=MIDDLE  ALT=\"%28-9+-+sqrt%28108%29%29%2F3\"   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=-3+-+2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"-3+-+2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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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=%286+-+sqrt%2820%29%29%2F2 ALIGN=MIDDLE  ALT=\"%286+-+sqrt%2820%29%29%2F2\"   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%2820%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%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=sqrt%2820%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%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 20\r<BR>\n" );
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document.write( "Factors:\r<BR>\n" );
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document.write( "1, 2, 4, 5, 10,\r<BR>\n" );
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document.write( "Notice how 4 is the largest perfect square, so lets break 20 down into 4*5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%2A5%29 ALIGN=MIDDLE  ALT=\"sqrt%284%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 20 into 4*5<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%284%29%2Asqrt%285%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%285%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%285%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%2820%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%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%285%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%285%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=%286+-+2%2Asqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"%286+-+2%2Asqrt%285%29%29%2F2\"   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=6%2F2+-+2%2Asqrt%285%29%2F2 ALIGN=MIDDLE  ALT=\"6%2F2+-+2%2Asqrt%285%29%2F2\"   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=3+-+2%2Asqrt%285%29%2F2 ALIGN=MIDDLE  ALT=\"3+-+2%2Asqrt%285%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F2 ALIGN=MIDDLE  ALT=\"6%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   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=3+-+sqrt%285%29 ALIGN=MIDDLE  ALT=\"3+-+sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F2 ALIGN=MIDDLE  ALT=\"2%2F2\"   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( "So the expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286+-+sqrt%2820%29%29%2F2 ALIGN=MIDDLE  ALT=\"%286+-+sqrt%2820%29%29%2F2\"   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=3+-+sqrt%285%29 ALIGN=MIDDLE  ALT=\"3+-+sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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