document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=139361>Question 139361</A>: <I><SPAN STYLE=\"word-break: break-all;\"> rationalize the denominator of the fraction.3 sqrt 3 over 3 sqrt 7 i came up with 3 sqrt 147 over 7 but i have no idea if this is correct.thanks in advance for your help .also rewrite 5 sqrt c with a small 2 at the top of the c.for this one i got c 2/5  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101604 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=101604\">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=%283sqrt%283%29%29%2F%283sqrt%287%29%29 ALIGN=MIDDLE  ALT=\"%283sqrt%283%29%29%2F%283sqrt%287%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Unless the number under the radical is a perfect square, like 4, 9, 16, 25..., then the square root is an irrational number.  A rational number is one that can be expressed as the quotient of two integers, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Fq ALIGN=MIDDLE  ALT=\"p%2Fq\"   DISABLED_style= \"max-width:90%; height:auto;\" > where p and q are integers.  An irrational number cannot be expressed this way.\r<BR>\n" );
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document.write( "So rationalizing a denominator means 'get that nasty radical the heck out of my denominator'\r<BR>\n" );
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document.write( "In this problem, we need to multiply the denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%287%29 ALIGN=MIDDLE  ALT=\"sqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the denominator will become <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%287%29%2Asqrt%287%29=3%2A7=21 ALIGN=MIDDLE  ALT=\"3%2Asqrt%287%29%2Asqrt%287%29=3%2A7=21\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  BUT, we have to do so in such a way that we don't change the value of the overall fraction.  Since we know that anything multiplied by 1 is itself (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2A1=a ALIGN=MIDDLE  ALT=\"a%2A1=a\"   DISABLED_style= \"max-width:90%; height:auto;\" > no matter what a is), we can multiply the fraction by 1 in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%287%29%2Fsqrt%287%29 ALIGN=MIDDLE  ALT=\"sqrt%287%29%2Fsqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fa=1 ALIGN=MIDDLE  ALT=\"a%2Fa=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > no matter what a is).\r<BR>\n" );
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document.write( "But first a rule about radicals:  No matter what a and b are (as long as they are positive) we can say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%29%2Asqrt%28b%29=sqrt%28ab%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%29%2Asqrt%28b%29=sqrt%28ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283sqrt%283%29%29%2F%283sqrt%287%29%29%29%28%28sqrt%287%29%29%2F%28sqrt%287%29%29%29=%283%2Asqrt%283%29%2Asqrt%287%29%29%2F%283%2Asqrt%287%29%2Asqrt%287%29%29=3%2Asqrt%2821%29%2F21 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So we have a new fraction that is equivalent to the original, but has a rational number (21) in the denominator.  Done.\r<BR>\n" );
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document.write( "For your other problem, I think you mean <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5sqrt%28c%5E2%29 ALIGN=MIDDLE  ALT=\"5sqrt%28c%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  I'm a little concerned that you are referring to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2 ALIGN=MIDDLE  ALT=\"c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, meaning 'c squared' as \"c with a small 2 at the top of the c\" and you are in a class where you are being asked to rationalize denominators.  The square root of something squared is just that thing, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28c%5E2%29=c ALIGN=MIDDLE  ALT=\"sqrt%28c%5E2%29=c\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and your simplified expression is just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5c ALIGN=MIDDLE  ALT=\"5c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  But my concern is that your rather unsophisticated use of terminology indicates that you might have a significant gap in your grasp of algebraic fundamentals that can't be corrected by visiting help sites like this one.  You should see your instructor and get him/her to provide you with some intensive remedial instruction.<BR>\n" );
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