document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=178266>Question 178266</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh>Algebra and Trigonometry Structure and Method book 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!\r<BR>\n" );
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document.write( "Binomials Containing Radicals<BR>\n" );
document.write( "Simplify. Assume that each radical represents a real number.<BR>\n" );
document.write( "(&#8730;(a-&#8730;a) *&#8730;(a+&#8730;a) )/( &#8730;(a-1))\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 #133233 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=133233\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, let's simplify the numerator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a-sqrt%28a%29%29%2Asqrt%28a%2Bsqrt%28a%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28a-sqrt%28a%29%29%2Asqrt%28a%2Bsqrt%28a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%28a%29 ALIGN=MIDDLE  ALT=\"x=sqrt%28a%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=sqrt%28a-sqrt%28a%29%29%2Asqrt%28a%2Bsqrt%28a%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28a-sqrt%28a%29%29%2Asqrt%28a%2Bsqrt%28a%29%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%28a-x%29%2Asqrt%28a%2Bx%29 ALIGN=MIDDLE  ALT=\"sqrt%28a-x%29%2Asqrt%28a%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%28a%29 ALIGN=MIDDLE  ALT=\"x=sqrt%28a%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=sqrt%28%28a-x%29%28a%2Bx%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28a-x%29%28a%2Bx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the roots using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28A%29%2Asqrt%28B%29=sqrt%28A%2AB%29 ALIGN=MIDDLE  ALT=\"sqrt%28A%29%2Asqrt%28B%29=sqrt%28A%2AB%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=sqrt%28a%5E2-x%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2-%28sqrt%28a%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2-%28sqrt%28a%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%28a%29 ALIGN=MIDDLE  ALT=\"x=sqrt%28a%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=sqrt%28a%5E2-a%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get \"a\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%28a-1%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%28a-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF \"a\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%29%2Asqrt%28a-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%29%2Asqrt%28a-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29 ALIGN=MIDDLE  ALT=\"sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this just the reverse of the previous identity)\r<BR>\n" );
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document.write( "So the numerator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a-sqrt%28a%29%29%2Asqrt%28a%2Bsqrt%28a%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28a-sqrt%28a%29%29%2Asqrt%28a%2Bsqrt%28a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%29%2Asqrt%28a-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%29%2Asqrt%28a-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now let's go back to the main problem:\r<BR>\n" );
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document.write( "So the expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28a-sqrt%28a%29%29%2Asqrt%28a%2Bsqrt%28a%29%29%29%2F%28sqrt%28a-1%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%28a-sqrt%28a%29%29%2Asqrt%28a%2Bsqrt%28a%29%29%29%2F%28sqrt%28a-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplifies to \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28a%29%2Asqrt%28a-1%29%29%2F%28sqrt%28a-1%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%28a%29%2Asqrt%28a-1%29%29%2F%28sqrt%28a-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (see steps above)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28a%29%2Ahighlight%28sqrt%28a-1%29%29%29%2F%28highlight%28sqrt%28a-1%29%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%28a%29%2Ahighlight%28sqrt%28a-1%29%29%29%2F%28highlight%28sqrt%28a-1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Highlight the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28a%29%2Across%28sqrt%28a-1%29%29%29%2F%28cross%28sqrt%28a-1%29%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%28a%29%2Across%28sqrt%28a-1%29%29%29%2F%28cross%28sqrt%28a-1%29%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%28a%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28a-sqrt%28a%29%29%2Asqrt%28a%2Bsqrt%28a%29%29%29%2F%28sqrt%28a-1%29%29=sqrt%28a%29 ALIGN=MIDDLE  ALT=\"%28sqrt%28a-sqrt%28a%29%29%2Asqrt%28a%2Bsqrt%28a%29%29%29%2F%28sqrt%28a-1%29%29=sqrt%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3E1 ALIGN=MIDDLE  ALT=\"a%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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