document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=338587>Question 338587</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 0 < n < 1, which of the following gives the correct ordering of<BR>\n" );
document.write( "&#8730;n, n, and, n^2 ?\r<BR>\n" );
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document.write( "A. &#8730;n < n < n^2<BR>\n" );
document.write( "b  &#8730;n < n^2 < n<BR>\n" );
document.write( "c  n <&#8730;n < n^2<BR>\n" );
document.write( "d  n < n^2 < &#8730;n <BR>\n" );
document.write( "e  n^2 < n < &#8730;n  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #242699 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=242699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If 0 < n < 1, which of the following gives the correct ordering of<BR>\n" );
document.write( "&#8730;n, n, and, n^2 ? <BR>\n" );
document.write( "A. &#8730;n < n < n^2<BR>\n" );
document.write( "b &#8730;n < n^2 < n<BR>\n" );
document.write( "c n <&#8730;n < n^2<BR>\n" );
document.write( "d n < n^2 < &#8730;n <BR>\n" );
document.write( "e n^2 < n < &#8730;n \r<BR>\n" );
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document.write( "&#8730;n = square root (sqrt) of n, n, and n^2, 0 < n < 1<BR>\n" );
document.write( "n = 0 --> sqrt(n) = 0, n^2 = 0, the values are all 0 and all equal<BR>\n" );
document.write( "n = 1 --> sqrt(n) = 1, n^2 = 1, the values are all 1 and all equal<BR>\n" );
document.write( "n = 0 and n = 1 are the end points of the interval (0,1) and are not included\r<BR>\n" );
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document.write( "checking 2 values of n<BR>\n" );
document.write( "n= 0.9 which is close to 1<BR>\n" );
document.write( "and n=10^(-6) which is close to 0\r<BR>\n" );
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document.write( "n = 0.9 = 9/10<BR>\n" );
document.write( "sqrt(n) = 3/(sqrt(10)) = (3sqrt(10))/10 = 0.9487 to 4 places<BR>\n" );
document.write( "n^2 = 81/100 = 0.81<BR>\n" );
document.write( "order: n^2, n, sqrt(n)<BR>\n" );
document.write( "n^2 < n < sqrt(n)<BR>\n" );
document.write( "n = 0.000001 = 1/1000000 = 1/(10^6) = 10^(-6)<BR>\n" );
document.write( "sqrt(n) = 10^(-3) = 0.001<BR>\n" );
document.write( "n^2 = 10^(-12) = 0.000000000001<BR>\n" );
document.write( "order: n^2, n, sqrt(n)<BR>\n" );
document.write( "n^2 < n < sqrt(n)\r<BR>\n" );
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document.write( "e n^2 < n < &#8730;n    is the answer when 0 < n < 1\r<BR>\n" );
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