document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=185800>Question 185800</A>: <I><SPAN STYLE=\"word-break: break-all;\">  &#8730;33/&#8730;77<BR>\n" );
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document.write( "Rationalize the denominator and simplify:  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139373 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=139373\">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%2833%29%2Fsqrt%2877%29 ALIGN=MIDDLE  ALT=\"sqrt%2833%29%2Fsqrt%2877%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=%28sqrt%2833%29%2Asqrt%2877%29%29%2F%28sqrt%2877%29%2Asqrt%2877%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%2833%29%2Asqrt%2877%29%29%2F%28sqrt%2877%29%2Asqrt%2877%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both the numerator and denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2877%29 ALIGN=MIDDLE  ALT=\"sqrt%2877%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=%28sqrt%2833%29%2Asqrt%2877%29%29%2F%2877%29 ALIGN=MIDDLE  ALT=\"%28sqrt%2833%29%2Asqrt%2877%29%29%2F%2877%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2877%29 ALIGN=MIDDLE  ALT=\"sqrt%2877%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2877%29 ALIGN=MIDDLE  ALT=\"sqrt%2877%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=77 ALIGN=MIDDLE  ALT=\"77\"   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=%28sqrt%283%2A11%29%2Asqrt%2811%2A7%29%29%2F%2877%29 ALIGN=MIDDLE  ALT=\"%28sqrt%283%2A11%29%2Asqrt%2811%2A7%29%29%2F%2877%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 33 into 3*11 and factor 77 into 11*7\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%2A11%2A11%2A7%29%29%2F%2877%29 ALIGN=MIDDLE  ALT=\"%28sqrt%283%2A11%2A11%2A7%29%29%2F%2877%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the roots.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%2A11%5E2%2A7%29%29%2F%2877%29 ALIGN=MIDDLE  ALT=\"%28sqrt%283%2A11%5E2%2A7%29%29%2F%2877%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%2Asqrt%2811%5E2%29%2Asqrt%287%29%29%2F%2877%29 ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%2Asqrt%2811%5E2%29%2Asqrt%287%29%29%2F%2877%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%2A11%2Asqrt%287%29%29%2F%2877%29 ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%2A11%2Asqrt%287%29%29%2F%2877%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%5E2 ALIGN=MIDDLE  ALT=\"11%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 11\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811%2Asqrt%283%2A7%29%29%2F%2877%29 ALIGN=MIDDLE  ALT=\"%2811%2Asqrt%283%2A7%29%29%2F%2877%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Recombine the square roots.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811%2Asqrt%2821%29%29%2F%2877%29 ALIGN=MIDDLE  ALT=\"%2811%2Asqrt%2821%29%29%2F%2877%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811%2Asqrt%2821%29%29%2F%287%2A11%29 ALIGN=MIDDLE  ALT=\"%2811%2Asqrt%2821%29%29%2F%287%2A11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 77 into 7*11\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%2811%29%2Asqrt%2821%29%29%2F%287%2Across%2811%29%29 ALIGN=MIDDLE  ALT=\"%28cross%2811%29%2Asqrt%2821%29%29%2F%287%2Across%2811%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2821%29%2F7 ALIGN=MIDDLE  ALT=\"sqrt%2821%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2833%29%2Fsqrt%2877%29=sqrt%2821%29%2F7 ALIGN=MIDDLE  ALT=\"sqrt%2833%29%2Fsqrt%2877%29=sqrt%2821%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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