document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117122>Question 117122</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85176 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=85176\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29%2F5-1%2Fsqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%29%2F5-1%2Fsqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29%2F5-%281%2Fsqrt%285%29%29%28sqrt%285%29%2Fsqrt%285%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%29%2F5-%281%2Fsqrt%285%29%29%28sqrt%285%29%2Fsqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the second fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2Fsqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2Fsqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Doing this will make \r<BR>\n" );
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document.write( "the denominator a rational number\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29%2F5-sqrt%285%29%2F%28sqrt%285%29sqrt%285%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%29%2F5-sqrt%285%29%2F%28sqrt%285%29sqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29%2F5-sqrt%285%29%2F5 ALIGN=MIDDLE  ALT=\"sqrt%2820%29%2F5-sqrt%285%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29sqrt%285%29=%28sqrt%285%29%29%5E2=5 ALIGN=MIDDLE  ALT=\"sqrt%285%29sqrt%285%29=%28sqrt%285%29%29%5E2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > shows \r<BR>\n" );
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document.write( "how the square undoes the square root.\r<BR>\n" );
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document.write( "Now that we have a rational denominator, and also a common denominator, we can combine the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2820%29-sqrt%285%29%29%2F5 ALIGN=MIDDLE  ALT=\"%28sqrt%2820%29-sqrt%285%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the numerators\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%284%2A5%29-sqrt%285%29%29%2F5 ALIGN=MIDDLE  ALT=\"%28sqrt%284%2A5%29-sqrt%285%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 20 into 4*5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%284%29%2Asqrt%285%29-sqrt%285%29%29%2F5 ALIGN=MIDDLE  ALT=\"%28sqrt%284%29%2Asqrt%285%29-sqrt%285%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the roots using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2Ay%29=sqrt%28x%29sqrt%28y%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2Ay%29=sqrt%28x%29sqrt%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Asqrt%285%29-sqrt%285%29%29%2F5 ALIGN=MIDDLE  ALT=\"%282%2Asqrt%285%29-sqrt%285%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect square 4 to get 2\r<BR>\n" );
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document.write( "Notice how we have the common term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282-1%29%2Asqrt%285%29%29%2F5 ALIGN=MIDDLE  ALT=\"%28%282-1%29%2Asqrt%285%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2F5 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29%2F5-1%2Fsqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%29%2F5-1%2Fsqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2F5 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29%2F5-1%2Fsqrt%285%29=sqrt%285%29%2F5 ALIGN=MIDDLE  ALT=\"sqrt%2820%29%2F5-1%2Fsqrt%285%29=sqrt%285%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "So looking at the answer you wrote, you are correct since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F5%29sqrt%285%29 ALIGN=MIDDLE  ALT=\"%281%2F5%29sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2F5 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "If we evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29%2F5-1%2Fsqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%29%2F5-1%2Fsqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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%2820%29%2F5-1%2Fsqrt%285%29=0.44721359549996 ALIGN=MIDDLE  ALT=\"sqrt%2820%29%2F5-1%2Fsqrt%285%29=0.44721359549996\"   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=sqrt%285%29%2F5 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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%285%29%2F5=0.44721359549996 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2F5=0.44721359549996\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice how these evaluate to the same value. So this shows that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%29%2F5-1%2Fsqrt%285%29=sqrt%285%29%2F5 ALIGN=MIDDLE  ALT=\"sqrt%2820%29%2F5-1%2Fsqrt%285%29=sqrt%285%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this verifies our \r<BR>\n" );
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document.write( "answer. </SPAN>\n" );
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