document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=51694>Question 51694</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How can I find the square root of 456 using the trial divisor method </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #34485 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1806)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><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=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=34485\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"><font size = 4><b>How can I find the square root of 456 using the \r\n" );
document.write( "trial divisor method?\r\n" );
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document.write( "Write 456 as 456.000000.  Then group it into pairs\r\n" );
document.write( "of digits, right and left of the decimal, Consider\r\n" );
document.write( "the introductory 4 to be the pair of digits 04. Each\r\n" );
document.write( "SINGLE digit of the answer will be placed over a PAIR\r\n" );
document.write( "of digits.\r\n" );
document.write( "           .  \r\n" );
document.write( "      ---------------\r\n" );
document.write( "     |04 56. 00 00 00\r\n" );
document.write( "        \r\n" );
document.write( "The largest digit that does not exceed the square root\r\n" );
document.write( "of the digit pair 04 is 2, so write 2 above the pair of \r\n" );
document.write( "digits 04. \r\n" );
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document.write( "       2               \r\n" );
document.write( "      ---------------\r\n" );
document.write( "     |04 56. 00 00 00\r\n" );
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document.write( "Square 2, getting 04.  Write it below the pair of digits 04\r\n" );
document.write( "Draw a line under it\r\n" );
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document.write( "       2   .    \r\n" );
document.write( "      ---------------\r\n" );
document.write( "     |04 56. 00 00 00\r\n" );
document.write( "      04\r\n" );
document.write( "      ---\r\n" );
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document.write( "Subtract getting 00 then bring down the next pair of digits\r\n" );
document.write( "56. Draw a vertical line to the left of 00 56\r\n" );
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document.write( "       2   .  \r\n" );
document.write( "      ---------------\r\n" );
document.write( "     |04 56. 00 00 00\r\n" );
document.write( "      04\r\n" );
document.write( "      ---\r\n" );
document.write( "     |00 56\r\n" );
document.write( "            \r\n" );
document.write( "So far we have 2 in the answer.  Multiply 2 by 20. (Double it\r\n" );
document.write( "and annex a 0).  This gives 40.  Write the 40 to the left of\r\n" );
document.write( "the vertical line:\r\n" );
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document.write( "       2   .            \r\n" );
document.write( "      ---------------\r\n" );
document.write( "     |04 56. 00 00 00\r\n" );
document.write( "       4\r\n" );
document.write( "      ---\r\n" );
document.write( "   40|00 56\r\n" );
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document.write( "40 is the TRIAL divisor.  Divide 40 into \"00 56\" (interpreted as\r\n" );
document.write( "just 56).  It goes 1+ times, so write 1 as the next digit in the \r\n" );
document.write( "answer.\r\n" );
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document.write( "       2  1.  \r\n" );
document.write( "      ---------------\r\n" );
document.write( "     |04 56. 00 00 00\r\n" );
document.write( "       4\r\n" );
document.write( "      ---\r\n" );
document.write( "   40|00 56\r\n" );
document.write( "                             \r\n" );
document.write( "Now to get the ACTUAL divisor, add the 1 to the the trial divisor,\r\n" );
document.write( "getting 41, and write this actual divisor under the 40 and place\r\n" );
document.write( "another vertical line to the right of it.\r\n" );
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document.write( "       2  1.  \r\n" );
document.write( "      ---------------\r\n" );
document.write( "     | 4 56. 00 00 00\r\n" );
document.write( "       4\r\n" );
document.write( "      ---\r\n" );
document.write( "   40|00 56\r\n" );
document.write( "   41|   \r\n" );
document.write( "         \r\n" );
document.write( "Multiply the 1 times the ACTUAL divisor, getting 41. Write it\r\n" );
document.write( "as \"00 41\" and write it beside the vertical line at the bottom\r\n" );
document.write( "underneath the 00 56. Draw a line underneath and subtract, getting\r\n" );
document.write( "15.  Then bring down the next pair of digits 00. Then draw a \r\n" );
document.write( "vertical line to the left of the 15.     \r\n" );
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document.write( "\r\n" );
document.write( "       2  1.  \r\n" );
document.write( "      ---------------\r\n" );
document.write( "     |04 56. 00 00 00\r\n" );
document.write( "       4\r\n" );
document.write( "      ---\r\n" );
document.write( "   40|00 56\r\n" );
document.write( "   41|00 41\r\n" );
document.write( "      -----\r\n" );
document.write( "        |15  00\r\n" );
document.write( "                   \r\n" );
document.write( "The digits in the answer so far are 21.  So multiply this by 20\r\n" );
document.write( "(Double 21, getting 42, then annex a 0 to get 420).  Write 420\r\n" );
document.write( "left of the vertical line.  420 is the next TRIAL divisor. \r\n" );
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document.write( "       2  1.    \r\n" );
document.write( "      ---------------\r\n" );
document.write( "     |04 56. 00 00 00\r\n" );
document.write( "       4\r\n" );
document.write( "      ---\r\n" );
document.write( "   40|00 56\r\n" );
document.write( "   41|   41\r\n" );
document.write( "      -----\r\n" );
document.write( "    420| 15  00\r\n" );
document.write( "                 \r\n" );
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document.write( "Divide the TRIAL divisor 420 into \"15 00\" (interpreted as\r\n" );
document.write( "1500).  It goes 3+ times, so write 3 as the next digit in the \r\n" );
document.write( "answer.\r\n" );
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document.write( "       2  1.  3    \r\n" );
document.write( "      ---------------\r\n" );
document.write( "     |04 56. 00 00 00\r\n" );
document.write( "       4\r\n" );
document.write( "      ---\r\n" );
document.write( "   40|00 56\r\n" );
document.write( "   41|   41\r\n" );
document.write( "      -----\r\n" );
document.write( "    420| 15  00\r\n" );
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document.write( "Now to get the next ACTUAL divisor, add the 3 to the the trial divisor,\r\n" );
document.write( "getting 423, and write this actual divisor under the 420 and place\r\n" );
document.write( "another vertical line to the right of it.\r\n" );
document.write( "\r\n" );
document.write( "       2  1.  3  \r\n" );
document.write( "      ---------------\r\n" );
document.write( "     |04 56. 00 00 00\r\n" );
document.write( "       4\r\n" );
document.write( "      ---\r\n" );
document.write( "   40|00 56\r\n" );
document.write( "   41|00 41\r\n" );
document.write( "      -----\r\n" );
document.write( "    420| 15  00\r\n" );
document.write( "    423| \r\n" );
document.write( "     \r\n" );
document.write( "Now multiply the 3 times the ACTUAL divisor, 423, getting 1296, and\r\n" );
document.write( "write it as \"12 96\" underneath the \"15 00\" and subtract, getting 231.\r\n" );
document.write( "So write this as \"02 31\", and draw a vertical line left of it \r\n" );
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document.write( "       2  1.  3  \r\n" );
document.write( "      ---------------\r\n" );
document.write( "     |04 56. 00 00 00\r\n" );
document.write( "       4\r\n" );
document.write( "      ---\r\n" );
document.write( "   40|00 56\r\n" );
document.write( "   41|00 41\r\n" );
document.write( "      -----\r\n" );
document.write( "    420| 15  00\r\n" );
document.write( "    423| 12  69\r\n" );
document.write( "        -------\r\n" );
document.write( "        |02  31 \r\n" );
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document.write( "The digits in the answer so far are 213.  So multiply this by 20\r\n" );
document.write( "(Double 213, getting 426, then annex a 0 to get 4260).  Write 4260\r\n" );
document.write( "left of the vertical line.  4260 is the next TRIAL divisor. \r\n" );
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document.write( "\r\n" );
document.write( "       2  1.  3  \r\n" );
document.write( "      ---------------\r\n" );
document.write( "     |04 56. 00 00 00\r\n" );
document.write( "       4\r\n" );
document.write( "      ---\r\n" );
document.write( "   40|00 56\r\n" );
document.write( "   41|00 41\r\n" );
document.write( "      -----\r\n" );
document.write( "    420| 15  00\r\n" );
document.write( "    423| 12  69\r\n" );
document.write( "        -------\r\n" );
document.write( "    4260|02  31 00\r\n" );
document.write( "    4265|\r\n" );
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document.write( "Continue this process as long as you like. Here is the\r\n" );
document.write( "finished problem taken to the nearest thousandth:\r\n" );
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document.write( "       2  1.  3  5  4\r\n" );
document.write( "      ---------------\r\n" );
document.write( "     |04 56. 00 00 00\r\n" );
document.write( "       4\r\n" );
document.write( "      ---\r\n" );
document.write( "   40|00 56\r\n" );
document.write( "   41|00 41\r\n" );
document.write( "      -----\r\n" );
document.write( "    420| 15  00\r\n" );
document.write( "    423| 12  69\r\n" );
document.write( "        -------\r\n" );
document.write( "    4260|02  31 00\r\n" );
document.write( "    4265|02  13 25\r\n" );
document.write( "         ---------\r\n" );
document.write( "       42700|17 75 00\r\n" );
document.write( "       42704|17 08 16\r\n" );
document.write( "             --------\r\n" );
document.write( "                66 84\r\n" );
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document.write( "To get another decimal place annex another \"00\" pair\r\n" );
document.write( "to bring down.\r\n" );
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document.write( "Why does it work?  I won't show the whole thing. But\r\n" );
document.write( "here's an idea to get you started if you are interested.  \r\n" );
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document.write( "(10u + t)² = 100u² + 20tu + t\r\n" );
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document.write( "Notice that 20u is the coefficient of t in the second term.\r\n" );
document.write( "That is related to why we multiply u by 20 to get the TRIAL \r\n" );
document.write( "divisor 20tu.  The t on the end is related to why we must \r\n" );
document.write( "add the t to get the ACTUAL divisor.  \r\n" );
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document.write( "Edwin</PRE><BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );