document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175089>Question 175089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> is there somewhere on the internet where it could help me solve the question?\r<BR>\n" );
document.write( "\n" );
document.write( "    Here is one of the questions it says Remove the radical from the denominator of the following fraction without changing the value of the fraction. could you please explain this to me step by step and show me this method with an example? <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130187 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=130187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are describing a process called \"Rationalizing The Denominator\" which simply means to convert the fraction so that the denominator is a rational number.   The trick is to multiply the fraction by 1 in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fa ALIGN=MIDDLE  ALT=\"a%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is selected so that after the multiplication the denominator is a rational number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For example, rationalize the denominator of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  In order for the denominator to be rational, we need to multiply it by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so that is our value for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > in this case.  The process looks like this:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fsqrt%282%29%29%28sqrt%282%29%2Fsqrt%282%29%29=sqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"%281%2Fsqrt%282%29%29%28sqrt%282%29%2Fsqrt%282%29%29=sqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The process becomes a little more complex when you are faced with a denominator that is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B-b ALIGN=MIDDLE  ALT=\"a%2B-b\"   DISABLED_style= \"max-width:90%; height:auto;\" > where either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > (or both, for that matter) is irrational.  In this situation, say if we had <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-sqrt%283%29 ALIGN=MIDDLE  ALT=\"2-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a denominator, there is no simple number that we can use as a multiplier to convert this denominator to a rational number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "What you need to do is to recall the \"difference of two squares\" factorization, namely:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%28a-b%29=a%5E2-b%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%28a-b%29=a%5E2-b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  That means you can take something like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-sqrt%283%29 ALIGN=MIDDLE  ALT=\"2-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and multiply by it's conjugate,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Bsqrt%283%29 ALIGN=MIDDLE  ALT=\"2%2Bsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to arrive at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2-sqrt%283%29%5E2=4-3=1 ALIGN=MIDDLE  ALT=\"2%5E2-sqrt%283%29%5E2=4-3=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's do an example:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Rationalize: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%283%2Bsqrt%285%29%29 ALIGN=MIDDLE  ALT=\"2%2F%283%2Bsqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The conjugate of the denominator is <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;\" >, so we have to multiply the original fraction by 1 in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-sqrt%285%29%29%2F%283-sqrt%285%29%29 ALIGN=MIDDLE  ALT=\"%283-sqrt%285%29%29%2F%283-sqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, thus:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F%283%2Bsqrt%285%29%29%29%28%283-sqrt%285%29%29%2F%283-sqrt%285%29%29%29=%286-2%2Asqrt%285%29%29%2F%289-5%29=%286-2%2Asqrt%285%29%29%2F4=%283-sqrt%285%29%29%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You can read more about this at:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "http://www.math.unt.edu/mathlab/emathlab/How%20to%20Rationalize%20the%20Denominator%20of%20a%20Fraction.htm\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "http://www.helpalgebra.com/articles/rationalizedenominator.htm\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Or just Google \"rationalize the denominator\" for a bunch more. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );