document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72254>Question 72254</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072934662/algebrahomeworkh>Elementary Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Write in simplified form \r<BR>\n" );
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document.write( "the square root of 5/the square root of 2b </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51675 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=51675\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The problem is to simplify:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%2Ab%29 ALIGN=MIDDLE  ALT=\"sqrt%282%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let's first show the division of these two terms:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%285%29%29%2F%28sqrt%282%2Ab%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%285%29%29%2F%28sqrt%282%2Ab%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But it is normally considered bad form to leave a radical in the denominator.  Therefore,<BR>\n" );
document.write( "let's multiply this entire expression by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282%2Ab%29%29%2F%28sqrt%282%2Ab%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%282%2Ab%29%29%2F%28sqrt%282%2Ab%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "You may notice that this multiplier equals 1 because the numerator and denominator are identical.<BR>\n" );
document.write( "So by multiplying this times the original problem we are just multiplying the problem<BR>\n" );
document.write( "by an expression that equals 1.<BR>\n" );
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document.write( "This gives us:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28sqrt%285%29%29%2F%28sqrt%282%2Ab%29%29%29%2A%28%28sqrt%282%2Ab%29%29%2F%28sqrt%282%2Ab%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which combines to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%285%29%2Asqrt%282%2Ab%29%29%2F%28sqrt%282%2Ab%29%2Asqrt%282%2Ab%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%285%29%2Asqrt%282%2Ab%29%29%2F%28sqrt%282%2Ab%29%2Asqrt%282%2Ab%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "The product in the denominator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%2Ab%29%2Asqrt%282%2Ab%29 ALIGN=MIDDLE  ALT=\"sqrt%282%2Ab%29%2Asqrt%282%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and it equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ab ALIGN=MIDDLE  ALT=\"2%2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "So the expression becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%285%29%2Asqrt%282%2Ab%29%29%2F%282%2Ab%29 ALIGN=MIDDLE  ALT=\"%28sqrt%285%29%2Asqrt%282%2Ab%29%29%2F%282%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But by the rules of radical operations the product of the two terms in the numerator <BR>\n" );
document.write( "can be combined under a single radical sign to give:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%2A2%2Ab%29%2F%282%2Ab%29 ALIGN=MIDDLE  ALT=\"sqrt%285%2A2%2Ab%29%2F%282%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and finally multiply the two terms inside the radical sign to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2810%2Ab%29%2F%282%2Ab%29 ALIGN=MIDDLE  ALT=\"sqrt%2810%2Ab%29%2F%282%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is an acceptable answer, but if you prefer, you can also write it as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%282%2Ab%29%29%2Asqrt%2810%2Ab%29 ALIGN=MIDDLE  ALT=\"%281%2F%282%2Ab%29%29%2Asqrt%2810%2Ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the processes involved in messing around with radicals.<BR>\n" );
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