document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113881>Question 113881</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify.  This is all one square root.\r<BR>\n" );
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document.write( "square root 3x/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83660 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=83660\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283x%2F2%29 ALIGN=MIDDLE  ALT=\"sqrt%283x%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is what I think you mean.\r<BR>\n" );
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document.write( "Begin with the fact that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%2Fb%29=sqrt%28a%29%2Fsqrt%28b%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%2Fb%29=sqrt%28a%29%2Fsqrt%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all real a, and real b so long as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%3C%3E0 ALIGN=MIDDLE  ALT=\"b%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283x%2F2%29=sqrt%283x%29%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%283x%2F2%29=sqrt%283x%29%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However, simplest form requires that you have no radicals in the denominator, so you have to perform a process called 'rationalizing the denominator.'  To perform this process, you need to start with the ideas that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2A+1=a ALIGN=MIDDLE  ALT=\"a+%2A+1=a\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all real a and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fa=1 ALIGN=MIDDLE  ALT=\"a%2Fa=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all real a, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3C%3E0 ALIGN=MIDDLE  ALT=\"a%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  What we are going to do is multiply our expression by 1 in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2Fsqrt%282%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=%28sqrt%283x%29%2Fsqrt%282%29%29%28sqrt%282%29%2Fsqrt%282%29%29=%28sqrt%283x%29sqrt%282%29%29%2Fsqrt%282%29sqrt%282%29=sqrt%286x%29%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And that is the simplest form for the given expression.\r<BR>\n" );
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document.write( "Hope that helps,<BR>\n" );
document.write( "John </SPAN>\n" );
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