document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201162>Question 1201162</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is probably a really stupid question. Please bear with me.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I was reading this article<BR>\n" );
document.write( "https://www.mathsisfun.com/algebra/square-root.html<BR>\n" );
document.write( "It's helping me learn a lot. The professor mentions the rule sqrt(xy) = sqrt(x)sqrt(y) then says \"but only when x and y are both greater than or equal to 0\"\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "But then there's this article<BR>\n" );
document.write( "https://www.mathsisfun.com/numbers/imaginary-numbers.html<BR>\n" );
document.write( "She or he breaks up the -9 into 9 x -1 and uses the square root rule only meant for positive numbers. <BR>\n" );
document.write( "What gives? Why is the -1 allowed? \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I don't understand sqrt(xy) = sqrt(x)sqrt(y) for x > 0 y > 0 but it clearly works(?) for negative numbers also. <BR>\n" );
document.write( "I suppose I don't really understand imaginary numbers too much. I appreciate you reading this and helping me out. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835421 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835421\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The statement from the professor in the first article you cite is incorrect -- or you misread the article.<br><BR>\n" );
document.write( "(NOTE: I looked at the article.  It seems poorly written and therefore confusing....)<br><BR>\n" );
document.write( "The correct rule is that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28xy%29=%28sqrt%28x%29%29%28sqrt%28y%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28xy%29=%28sqrt%28x%29%29%28sqrt%28y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all cases EXCEPT when x and y are BOTH negative.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%282%29%282%29%29=sqrt%284%29=2 ALIGN=MIDDLE  ALT=\"sqrt%28%282%29%282%29%29=sqrt%284%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2Asqrt%282%29=2 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2Asqrt%282%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the results are the same<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%284%29%28-1%29%29=sqrt%28-4%29=2i ALIGN=MIDDLE  ALT=\"sqrt%28%284%29%28-1%29%29=sqrt%28-4%29=2i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29%2Asqrt%28-1%29=%282%29%28i%29=2i ALIGN=MIDDLE  ALT=\"sqrt%284%29%2Asqrt%28-1%29=%282%29%28i%29=2i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the results are the same<br><BR>\n" );
document.write( "But<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%29%2Asqrt%28-1%29=%28i%29%28i%29=i%5E2=-1 ALIGN=MIDDLE  ALT=\"sqrt%28-1%29%2Asqrt%28-1%29=%28i%29%28i%29=i%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28-1%29%28-1%29%29=sqrt%281%29=1 ALIGN=MIDDLE  ALT=\"sqrt%28%28-1%29%28-1%29%29=sqrt%281%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the results are different -- because both numbers are negative<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );