document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=249026>Question 249026</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am struggling with this one ....any help is much appreciated!\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "Square root of 5 over the square root of 180\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181437 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=181437\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's one way to do it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2Fsqrt%28180%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2Fsqrt%28180%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%285%2F180%29 ALIGN=MIDDLE  ALT=\"sqrt%285%2F180%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%28x%29%2Fsqrt%28y%29=sqrt%28x%2Fy%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29%2Fsqrt%28y%29=sqrt%28x%2Fy%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%281%2F36%29 ALIGN=MIDDLE  ALT=\"sqrt%281%2F36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281%29%2Fsqrt%2836%29 ALIGN=MIDDLE  ALT=\"sqrt%281%29%2Fsqrt%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2Fy%29=sqrt%28x%29%2Fsqrt%28y%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2Fy%29=sqrt%28x%29%2Fsqrt%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie it's the reverse of the other identity)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fsqrt%2836%29 ALIGN=MIDDLE  ALT=\"1%2Fsqrt%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 1 to get 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 36 to get 6.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2Fsqrt%28180%29=1%2F6 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2Fsqrt%28180%29=1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==========================================================================\r<BR>\n" );
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document.write( "Or...\r<BR>\n" );
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document.write( "Here's another way to do it. This method is more common as it works better in general.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2Fsqrt%28180%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2Fsqrt%28180%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "The goal is to get the denominator equal to a rational number. To do this, we multiply the denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28180%29 ALIGN=MIDDLE  ALT=\"sqrt%28180%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We must do the same for the numerator as well.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%285%29%2Asqrt%28180%29%29%2F%28sqrt%28180%29%2Asqrt%28180%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%285%29%2Asqrt%28180%29%29%2F%28sqrt%28180%29%2Asqrt%28180%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both the numerator and denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28180%29 ALIGN=MIDDLE  ALT=\"sqrt%28180%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<font color=red>------------------------------------------\r<BR>\n" );
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document.write( "Scratch Work</font>\r<BR>\n" );
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document.write( "Take note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28180%29%2Asqrt%28180%29=sqrt%28180%2A180%29 ALIGN=MIDDLE  ALT=\"sqrt%28180%29%2Asqrt%28180%29=sqrt%28180%2A180%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (it's like those previous identities). Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28180%29%2Asqrt%28180%29=sqrt%28180%2A180%29 ALIGN=MIDDLE  ALT=\"sqrt%28180%29%2Asqrt%28180%29=sqrt%28180%2A180%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28180%29%2Asqrt%28180%29=sqrt%28180%2A180%29=sqrt%28180%5E2%29=180 ALIGN=MIDDLE  ALT=\"sqrt%28180%29%2Asqrt%28180%29=sqrt%28180%2A180%29=sqrt%28180%5E2%29=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "For the last step of that equation, the square root 'undoes' the square. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%29=x ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=0 ALIGN=MIDDLE  ALT=\"x%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In the end, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28180%29%2Asqrt%28180%29=180 ALIGN=MIDDLE  ALT=\"sqrt%28180%29%2Asqrt%28180%29=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<font color=red>------------------------------------------</font>\r<BR>\n" );
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document.write( "Now back to the problem at hand....\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%285%29%2Asqrt%28180%29%29%2F180 ALIGN=MIDDLE  ALT=\"%28sqrt%285%29%2Asqrt%28180%29%29%2F180\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28180%29 ALIGN=MIDDLE  ALT=\"sqrt%28180%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28180%29 ALIGN=MIDDLE  ALT=\"sqrt%28180%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 180 (see scratch work above).\r<BR>\n" );
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document.write( "<font color=red>------------------------------------------\r<BR>\n" );
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document.write( "More Scratch Work</font>\r<BR>\n" );
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document.write( "Following the same idea, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2Asqrt%28180%29=sqrt%285%2A180%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2Asqrt%28180%29=sqrt%285%2A180%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > due to the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29\"   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%285%29%2Asqrt%28180%29=sqrt%285%2A180%29=sqrt%28900%29=sqrt%2830%5E2%29=30 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2Asqrt%28180%29=sqrt%285%2A180%29=sqrt%28900%29=sqrt%2830%5E2%29=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In the end, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2Asqrt%28180%29=30 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2Asqrt%28180%29=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you're not sure about your work, a calculator will come in handy to check your work.\r<BR>\n" );
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document.write( "<font color=red>------------------------------------------</font>\r<BR>\n" );
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document.write( "Now back to the problem at hand....\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F180 ALIGN=MIDDLE  ALT=\"30%2F180\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <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;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28180%29 ALIGN=MIDDLE  ALT=\"sqrt%28180%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 30 (see scratch work above).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce the fraction.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2Fsqrt%28180%29=1%2F6 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2Fsqrt%28180%29=1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > regardless of the method used to get the answer. </SPAN>\n" );
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