document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=36954>Question 36954</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need help understand these.\r<BR>\n" );
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document.write( "2)	Is ( square root of x)^2=x   an identity (true for all nonnegative values of x)?<BR>\n" );
document.write( "Answer:  <BR>\n" );
document.write( "Explain your answer in this space.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27136 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27136\">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=%28sqrt%28x%29%29%5E2=x ALIGN=MIDDLE  ALT=\"%28sqrt%28x%29%29%5E2=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an identity.\r<BR>\n" );
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document.write( "ILLUSTRATION: <BR>\n" );
document.write( "Suppose x = 8, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288%29 ALIGN=MIDDLE  ALT=\"sqrt%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%282%29 ALIGN=MIDDLE  ALT=\"2sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2sqrt%282%29 ALIGN=MIDDLE  ALT=\"-2sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Now, as both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282sqrt%282%29%29%5E2 ALIGN=MIDDLE  ALT=\"%282sqrt%282%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2sqrt%282%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28-2sqrt%282%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > are equal to 8 (= x) hence the truth of the statement made above can easily be verified.\r<BR>\n" );
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document.write( "However, if x be a negative number, say, x = -4. <BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-4%29 ALIGN=MIDDLE  ALT=\"sqrt%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is imaginery and equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2i ALIGN=MIDDLE  ALT=\"2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > [where i = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >]. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%28x%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282i%29%5E2 ALIGN=MIDDLE  ALT=\"%282i%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4i%5E2 ALIGN=MIDDLE  ALT=\"4i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -4 = x.<BR>\n" );
document.write( "Thus, the proposition is also valid for negative real values of 'x'. </SPAN>\n" );
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