document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133112>Question 133112</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the following.  Assume that variables can represent any real numbers.\r<BR>\n" );
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document.write( "sqrt ( a+4 )^2\r<BR>\n" );
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document.write( "The a+4 should be in parenthesis with an exponent of 2 in a radical sign.  I hope I explained that correctly. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97328 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=97328\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you have something like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=4 ALIGN=MIDDLE  ALT=\"x%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, how do you solve this? Well you simply take the square root of both sides like this\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%29=sqrt%284%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%29=sqrt%284%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=x=0%2B-sqrt%284%29 ALIGN=MIDDLE  ALT=\"x=0%2B-sqrt%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. What's happening is the square root is undoing the square exponent. \r<BR>\n" );
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document.write( "---------------------\r<BR>\n" );
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document.write( "So the same thing is happening with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+%28+a%2B4+%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28+%28+a%2B4+%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If you can't see it, then let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=a%2B4 ALIGN=MIDDLE  ALT=\"x=a%2B4\"   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=sqrt%28x%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so this simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > where x is positive\r<BR>\n" );
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document.write( "Now plug <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B4 ALIGN=MIDDLE  ALT=\"a%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > into x to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B4 ALIGN=MIDDLE  ALT=\"a%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+%28+a%2B4+%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28+%28+a%2B4+%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B4 ALIGN=MIDDLE  ALT=\"a%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > . In other words,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+%28+a%2B4+%29%5E2%29=a%2B4 ALIGN=MIDDLE  ALT=\"sqrt%28+%28+a%2B4+%29%5E2%29=a%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B4%3E0 ALIGN=MIDDLE  ALT=\"a%2B4%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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