document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1078374>Question 1078374</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone assist me with this problem on my homework.\r<BR>\n" );
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document.write( "Suppose that x is not a perfect square and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5E2+ ALIGN=MIDDLE  ALT=\"+a%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the nearest perfect square to x. For a rough<BR>\n" );
document.write( "estimate of the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+x+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find the value of<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5B1%5D=%0D%0A1%2F2 ALIGN=MIDDLE  ALT=\"+y%5B1%5D=%0D%0A1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28a%2Bx%2Fa%29+ ALIGN=MIDDLE  ALT=\"+%28a%2Bx%2Fa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This estimate can be improved by<BR>\n" );
document.write( "calculating a second estimate using the first estimate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5B1%5D+ ALIGN=MIDDLE  ALT=\"+y%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > in place of a: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5B2%5D=+1%2F2+ ALIGN=MIDDLE  ALT=\"+y%5B2%5D=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28y%5B1%5D%2B+x%2Fy%5B1%5D%29+ ALIGN=MIDDLE  ALT=\"+%28y%5B1%5D%2B+x%2Fy%5B1%5D%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Repeating this process several times will give more and more accurate estimates of x .<BR>\n" );
document.write( "1. a. Which perfect square is closest to 80?<BR>\n" );
document.write( "b. Use Heron’s method for approximating square roots to calculate the first estimate of the<BR>\n" );
document.write( "square root of 80. Give an exact decimal answer.<BR>\n" );
document.write( "c. Use the first estimate of the square root of 80 to find a more refined second estimate.<BR>\n" );
document.write( "Round this second estimate to 6 decimal places.<BR>\n" );
document.write( "d. Use a calculator to find the actual value of the square root of 80. List all digits shown on<BR>\n" );
document.write( "your calculator’s display.<BR>\n" );
document.write( "e. Compare the actual value from part (d) to the values of the first and second estimates.<BR>\n" );
document.write( "What do you notice?<BR>\n" );
document.write( "f. How many iterations of this process are necessary to get an estimate that differs no more<BR>\n" );
document.write( "than one digit from the actual value recorded in part (d)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #692871 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=692871\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E2=81 ALIGN=MIDDLE  ALT=\"9%5E2=81\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=9 ALIGN=MIDDLE  ALT=\"a=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=80 ALIGN=MIDDLE  ALT=\"x=80\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you're looking for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2880%29 ALIGN=MIDDLE  ALT=\"sqrt%2880%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=%281%2F2%29%289%2B80%2F9%29=%281%2F2%29%2881%2F9%2B80%2F9%29=%281%2F2%29%28161%2F9%29=161%2F18 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D=%281%2F2%29%28161%2F18%2B80%2F%28161%2F18%29%29=%281%2F2%29%28161%2F18%2B1440%2F161%29=%281%2F2%29%2851841%2F2898%29=51841%2F5796 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There's a start.<BR>\n" );
document.write( "Work through the rest of the problem.  </SPAN>\n" );
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