document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248888>Question 248888</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi. My question is how do I write the following in simplified radical form by rationalizing the denominator?  \r<BR>\n" );
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document.write( " 2sqrt2+1<BR>\n" );
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document.write( "-5sqrt2+3\r<BR>\n" );
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document.write( "I've been at it for 2 hours. I've tried using the conjugate but it's confusing because it seems to be written in a different form than the textbook. I've gotten 2 different answers, the latest one being:\r<BR>\n" );
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document.write( "-3-21sqrt2<BR>\n" );
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document.write( "    41\r<BR>\n" );
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document.write( "I'm not sure if I doing this right. If someone could help me, it would be greatly appreciated. Thank you.\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 #181358 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=181358\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Asqrt%282%29+%2B+1%29+%2F+%28-5%2Asqrt%282%29+%2B+3%29 ALIGN=MIDDLE  ALT=\"%282%2Asqrt%282%29+%2B+1%29+%2F+%28-5%2Asqrt%282%29+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the conjugate of the denominator would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%2Asqrt%282%29+-+3%29 ALIGN=MIDDLE  ALT=\"%28-5%2Asqrt%282%29+-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "multiply the expression by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%2Asqrt%282%29+-+3%29+%2F+%28-5%2Asqrt%282%29+-+3%29 ALIGN=MIDDLE  ALT=\"%28-5%2Asqrt%282%29+-+3%29+%2F+%28-5%2Asqrt%282%29+-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282%2Asqrt%282%29+%2B+1%29+%2A+%28-5%2Asqrt%282%29+-+3%29%29+%2F+%28%28-5%2Asqrt%282%29+%2B+3%29+%2A+%28-5%2Asqrt%282%29+-+3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "perform the indicated operations to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-23+-+11%2Asqrt%282%29%29+%2F+41 ALIGN=MIDDLE  ALT=\"%28-23+-+11%2Asqrt%282%29%29+%2F+41\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you got the denominator ok.\r<BR>\n" );
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document.write( "you got pieces of the numerator ok but something went wrong somewhere.\r<BR>\n" );
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document.write( "the numerator became:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282%2Asqrt%282%29+%2B+1%29+%2A+%28-5%2Asqrt%282%29+-+3%29%29 ALIGN=MIDDLE  ALT=\"%28%282%2Asqrt%282%29+%2B+1%29+%2A+%28-5%2Asqrt%282%29+-+3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "multiplying these terms together you would get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%282%29+%2A+-5%2Asqrt%282%29+=+-10%2Asqrt%282%29%5E2+=+-10%2A2+=+-20 ALIGN=MIDDLE  ALT=\"2%2Asqrt%282%29+%2A+-5%2Asqrt%282%29+=+-10%2Asqrt%282%29%5E2+=+-10%2A2+=+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%282%29+%2A+-3+=+-6%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%282%29+%2A+-3+=+-6%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2A+-5%2Asqrt%282%29+=+-5%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"1+%2A+-5%2Asqrt%282%29+=+-5%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2A+-3+=+-3 ALIGN=MIDDLE  ALT=\"1+%2A+-3+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "combining like terms you would get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-23-11%2Asqrt%282%29%29 ALIGN=MIDDLE  ALT=\"%28-23-11%2Asqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "your answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-23-11%2Asqrt%282%29%29%2F41 ALIGN=MIDDLE  ALT=\"%28-23-11%2Asqrt%282%29%29%2F41\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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