document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=86811>Question 86811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify:\r<BR>\n" );
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document.write( "square root of 500 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #62806 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=62806\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since 500 is an even number you know that it is divisible by 2.  Therefore, you can write<BR>\n" );
document.write( "it as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500+=+250+%2A+2 ALIGN=MIDDLE  ALT=\"500+=+250+%2A+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But 250 is also even and divisible by 2. So 250 can be replaced by 125 * 2. Therefore,<BR>\n" );
document.write( "you can replace 500 by 125*2*2 which is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500+=+125%2A2%5E2 ALIGN=MIDDLE  ALT=\"500+=+125%2A2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125+=+5%2A5%2A5+=+5%2A5%5E2 ALIGN=MIDDLE  ALT=\"125+=+5%2A5%2A5+=+5%2A5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So if you substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A5%5E2 ALIGN=MIDDLE  ALT=\"5%2A5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > for 125 you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500+=+5%2A5%5E2%2A2%5E2 ALIGN=MIDDLE  ALT=\"500+=+5%2A5%5E2%2A2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Taking the square root of all three terms in this multiplication string results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28500%29=+sqrt%285%2A5%5E2%2A2%5E2%29+=+sqrt%285%29%2Asqrt%285%5E2%29%2Asqrt%282%5E2%29+=+sqrt%285%29%2A5%2A2+=+10%2Asqrt%285%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the simplified form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28500%29 ALIGN=MIDDLE  ALT=\"sqrt%28500%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"10%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Had you recognized it earlier, you could have written:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28500%29+=+sqrt%28100%2A5%29+=+sqrt%28100%29%2Asqrt%285%29+=+10%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%28500%29+=+sqrt%28100%2A5%29+=+sqrt%28100%29%2Asqrt%285%29+=+10%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "much quicker, but not as much practice as the long way.<BR>\n" );
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document.write( "Hope this helps you to see how square root problems such as this one can be simplified.<BR>\n" );
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