document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=274775>Question 274775</A>: <I><SPAN STYLE=\"word-break: break-all;\"> simplify by factoring  4&#8730;486 is </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #200504 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=200504\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, let's simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28486%29 ALIGN=MIDDLE  ALT=\"sqrt%28486%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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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. When you take the square root of this perfect square, you will get a rational number.\r<BR>\n" );
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document.write( "So let's list the factors of 486\r<BR>\n" );
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document.write( "Factors:\r<BR>\n" );
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document.write( "1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486\r<BR>\n" );
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document.write( "Notice how 81 is the largest perfect square, so lets factor 486 into 81*6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2881%2A6%29 ALIGN=MIDDLE  ALT=\"sqrt%2881%2A6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 486 into 81*6<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2881%29%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%2881%29%2Asqrt%286%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=9%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"9%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect square 81 to get 9 <BR>\n" );
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document.write( "So the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28486%29 ALIGN=MIDDLE  ALT=\"sqrt%28486%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"9%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28486%29=9%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%28486%29=9%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%28486%29=4%2A9%2Asqrt%286%29=36%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%28486%29=4%2A9%2Asqrt%286%29=36%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%28486%29=36%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%28486%29=36%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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