document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153897>Question 1153897</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Calculate by means of the binomial theorem the value of(16.32)^1/2 to 5 decimal places </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #776223 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=776223\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Here are the first few terms of the expansion of (a+b)^n using the binomial theorem.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28n%2C0%29%2A%28%28a%5En%29%28b%5E0%29%29+%2B+C%28n%2C1%29%2A%28%28a%5E%28n-1%29%29%28b%5E1%29%29+%2B+C%28n%2C2%29%2A%28%28a%5E%28n-2%29%29%28b%5E2%29%29+%2B+C%28n%2C3%29%2A%28%28a%5E%28n-3%29%29%28b%5E3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "When n is not a positive integer, we want to write the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28n%2Cr%29 ALIGN=MIDDLE  ALT=\"C%28n%2Cr%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > numbers in expanded form:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28n%2C0%29+=+1 ALIGN=MIDDLE  ALT=\"C%28n%2C0%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28n%2C1%29+=+n%2F1%21 ALIGN=MIDDLE  ALT=\"C%28n%2C1%29+=+n%2F1%21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28n%2C2%29+=+%28n%28n-1%29%29%2F2%21%29 ALIGN=MIDDLE  ALT=\"C%28n%2C2%29+=+%28n%28n-1%29%29%2F2%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "etc....<br><BR>\n" );
document.write( "Then the first few terms of the expansion are<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5En+=+a%5En+%2B+%28%28n%29%2F1%21%29%28%28a%5E%28n-1%29%29%28b%5E1%29%29+%2B+%28%28%28n%29%28n-1%29%29%2F2%21%29%28%28a%5E%28n-2%29%29%28b%5E2%29%29+%2B+%28%28%28n%29%28n-1%29%28n-2%29%29%2F3%21%29%28%28a%5E%28n-3%29%29%28b%5E3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now we can plug in n=0.5, a=16, and b=0.32 to find the square root of 16.32 to several decimal places.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5En+=+16%5E0.5+=+4 ALIGN=MIDDLE  ALT=\"a%5En+=+16%5E0.5+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n%29%2F1%21%29%28%28a%5E%28n-1%29%29%28b%5E1%29%29+=+%28.5%2F1%29%28%28%2816%29%5E%28-0.5%29%29%28.32%5E1%29%29+=+.04 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28n%29%28n-1%29%29%2F2%21%29%28%28a%5E%28n-2%29%29%28b%5E2%29%29+=+%28%28%28.5%29%28-.5%29%29%2F2%29%28%28%2816%29%5E%28-1.5%29%29%28.32%5E2%29%29+=+-0.0002 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28n%29%28n-1%29%28n-2%29%29%2F3%21%29%28%28a%5E%28n-3%29%29%28b%5E3%29%29+=+%28%28%28.5%29%28-.5%29%28-1.5%29%29%2F6%29%28%28%2816%29%5E%28-2.5%29%29%28.32%5E3%29%29+=+0.000002 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So we have the square root of 16.32, using the first four terms of the binomial expansion of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%2B.32%29%5E0.5 ALIGN=MIDDLE  ALT=\"%2816%2B.32%29%5E0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, as being<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B.04-.0002%2B.000002+=+4.039802 ALIGN=MIDDLE  ALT=\"4%2B.04-.0002%2B.000002+=+4.039802\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The actual value to 9 decimal places is 4.039801975, so our approximation is good to 6 decimal places.<br><BR>\n" );
document.write( " </SPAN>\n" );
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