document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=718131>Question 718131</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rationalize the numerator for the following expression.\r<BR>\n" );
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document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281+-+sqrt%283%29%29%2F3+ ALIGN=MIDDLE  ALT=\"+%281+-+sqrt%283%29%29%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28sqrt%28p%29%2Bsqrt%28p%5E2-1%29%29%2F%28sqrt%28p%29-sqrt%28p%5E2-1%29%29+ ALIGN=MIDDLE  ALT=\"+%28sqrt%28p%29%2Bsqrt%28p%5E2-1%29%29%2F%28sqrt%28p%29-sqrt%28p%5E2-1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #440853 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=440853\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) 3 is rational<BR>\n" );
document.write( "b) Multiply the numerator and denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28p%29%2Bsqrt%28p%5E2-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28p%29%2Bsqrt%28p%5E2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will be easier if you think of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28p%29 ALIGN=MIDDLE  ALT=\"sqrt%28p%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as \"a\" and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28p%5E2-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28p%5E2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as \"b\" and use the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > pattern to multiply the numerators and the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-b%29%28a%2Bb%29+=+a%5E2-b%5E2 ALIGN=MIDDLE  ALT=\"%28a-b%29%28a%2Bb%29+=+a%5E2-b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > pattern to multiply the denominators. (The second pattern, in fact, is how you figure out that multiplying by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28p%29%2Bsqrt%28p%5E2-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28p%29%2Bsqrt%28p%5E2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > will help. We already have a (\"a\"-\"b\"). If we multiply by the corresponding (\"a\"+\"b\") we will get and expression of only perfect squares, making the square roots disappear!) </SPAN>\n" );
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