document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206442>Question 1206442</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm working on half-angle identities for trigonometry and I keep getting the wrong answer, or possibly in a different form than the book's answer.\r<BR>\n" );
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document.write( "I'll just ask about the answer which is basically rationalizing a root problem (with a fractional root within it).\r<BR>\n" );
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document.write( "I keep getting stuck on an intermediary step, as follows, from the solution in the book:\r<BR>\n" );
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document.write( "sqrt(1+sqrt(5))/sqrt2\r<BR>\n" );
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document.write( "which gives the solution:\r<BR>\n" );
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document.write( "sqrt(50-10sqrt(5))/10\r<BR>\n" );
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document.write( "I know I'm messing up with rationalizing the denominator and I can't figure it out.\r<BR>\n" );
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document.write( "I ran the plain text radicals above in Wolfram Alpha and it comes out basically as the problem/solution in the book.\r<BR>\n" );
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document.write( "Any help would be greatly appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843923 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=843923\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
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document.write( "The student has corrected the given expression.  See further down for how the given answer is the correct equivalent form of the given expression.<br><BR>\n" );
document.write( "Note also that the sign in the solution is \"+\", not \"-\".<br><BR>\n" );
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document.write( "The answer you show is not equivalent to the given expression; perhaps in your book you are looking at the answer to a different problem.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281%2Bsqrt%285%29%29%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%281%2Bsqrt%285%29%29%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.272 to 3 decimal places<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850-10sqrt%285%29%29%2F10 ALIGN=MIDDLE  ALT=\"sqrt%2850-10sqrt%285%29%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.526 to 3 decimal places<br><BR>\n" );
document.write( "To rationalize the denominator in the given expression, we only need to multiply numerator and denominator by sqrt(2):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282%29%29%28sqrt%281%2Bsqrt%285%29%29%2Fsqrt%282%29%29=%28sqrt%282%2B2sqrt%285%29%29%29%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "-------------------------------------------------------------<br><BR>\n" );
document.write( "Corrected original expression: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281%2B%28sqrt%285%29%2F5%29%29%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%281%2B%28sqrt%285%29%2F5%29%29%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply numerator and denominator by sqrt(2):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%28sqrt%281%2B%28sqrt%285%29%2F5%29%29%29%2F2=sqrt%282%2B2sqrt%285%29%2F5%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%282%29%28sqrt%281%2B%28sqrt%285%29%2F5%29%29%29%2F2=sqrt%282%2B2sqrt%285%29%2F5%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Combine fractions inside the radical:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28%2810%2B2sqrt%285%29%29%2F5%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28sqrt%28%2810%2B2sqrt%285%29%29%2F5%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply numerator and denominator in the radical by 5 to rationalize the denominator in the radical; and simplify:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28%2850%2B10sqrt%285%29%29%2F25%29%29%2F2=%28%28sqrt%2850%2B10sqrt%285%29%29%29%2F5%29%2F2=%28sqrt%2850%2B10sqrt%285%29%29%29%2F10 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );