document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=217291>Question 217291</A>: <I><SPAN STYLE=\"word-break: break-all;\">      My brother in law is taking some courses, and asked me about this problem.\r<BR>\n" );
document.write( "\n" );
document.write( "Please solve this equation, and show how you did so. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt25344+=+48sqrt11 ALIGN=MIDDLE  ALT=\"sqrt25344+=+48sqrt11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "I know that there is a way to show how the sqrt25344 equals the other side, but the book he's using seems to be skipping a step on how they got part of the answer. \r<BR>\n" );
document.write( "\n" );
document.write( "Thanks,<BR>\n" );
document.write( "Dave </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163846 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=163846\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825344%29 ALIGN=MIDDLE  ALT=\"sqrt%2825344%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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. When you take the square root of this perfect square, you will get a rational number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So let's list the factors of 25344\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Factors:\r<BR>\n" );
document.write( "\n" );
document.write( "1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 32, 33, 36, 44, 48, 64, 66, 72, 88, 96, 99, 128, 132, 144, 176, 192, 198, 256, 264, 288, 352, 384, 396, 528, 576, 704, 768, 792, 1056, 1152, 1408, 1584, 2112, 2304, 2816, 3168, 4224, 6336, 8448, 12672, 25344\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice how 2304 is the largest perfect square, so lets factor 25344 into 2304*11\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282304%2A11%29 ALIGN=MIDDLE  ALT=\"sqrt%282304%2A11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 25344 into 2304*11<BR>\n" );
document.write( " <BR>\n" );
document.write( " <BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282304%29%2Asqrt%2811%29 ALIGN=MIDDLE  ALT=\"sqrt%282304%29%2Asqrt%2811%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" );
document.write( " <BR>\n" );
document.write( " <BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2Asqrt%2811%29 ALIGN=MIDDLE  ALT=\"48%2Asqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect square 2304 to get 48 <BR>\n" );
document.write( " <BR>\n" );
document.write( " <BR>\n" );
document.write( " <BR>\n" );
document.write( "So the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825344%29 ALIGN=MIDDLE  ALT=\"sqrt%2825344%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2Asqrt%2811%29 ALIGN=MIDDLE  ALT=\"48%2Asqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825344%29=48%2Asqrt%2811%29 ALIGN=MIDDLE  ALT=\"sqrt%2825344%29=48%2Asqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Check:\r<BR>\n" );
document.write( "\n" );
document.write( "Notice if we evaluate the square root of 25344 with a calculator we get\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825344%29=159.197989937059 ALIGN=MIDDLE  ALT=\"sqrt%2825344%29=159.197989937059\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and if we evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2Asqrt%2811%29 ALIGN=MIDDLE  ALT=\"48%2Asqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2Asqrt%2811%29=159.197989937059 ALIGN=MIDDLE  ALT=\"48%2Asqrt%2811%29=159.197989937059\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This shows that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825344%29=48%2Asqrt%2811%29 ALIGN=MIDDLE  ALT=\"sqrt%2825344%29=48%2Asqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this verifies our answer  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );