document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=575188>Question 575188</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the square root of 24 in the simplest radical form </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #369425 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=369425\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2824%29 ALIGN=MIDDLE  ALT=\"sqrt%2824%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\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 24\r<BR>\n" );
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document.write( "Factors:\r<BR>\n" );
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document.write( "1, 2, 3, 4, 6, 8, 12, 24\r<BR>\n" );
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document.write( "Notice how 4 is the largest perfect square, so lets factor 24 into 4*6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%2A6%29 ALIGN=MIDDLE  ALT=\"sqrt%284%2A6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 24 into 4*6<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%284%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=2%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%286%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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2824%29 ALIGN=MIDDLE  ALT=\"sqrt%2824%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "----------------------------<BR>\n" );
document.write( "Check:\r<BR>\n" );
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document.write( "Notice if we evaluate the square root of 24 with a calculator we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2824%29=4.89897948556636 ALIGN=MIDDLE  ALT=\"sqrt%2824%29=4.89897948556636\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and if we evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%286%29=4.89897948556636 ALIGN=MIDDLE  ALT=\"2%2Asqrt%286%29=4.89897948556636\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This shows that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2824%29=2%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%2824%29=2%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this verifies our answer  </SPAN>\n" );
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