document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=8481>Question 8481</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how shall i find the square root of 169 without using calculator?? please describe briefly.. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4684 by </B><A HREF=/tutors/aboutme.mpl?userid=bonster><B>bonster(299)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bonster><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=4684\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if you don't know it, think of the squared numbers that you already know and use them as markers...\r<BR>\n" );
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document.write( "for example, you might already know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%5E2 ALIGN=MIDDLE  ALT=\"12%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=144 and you might already know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%5E2 ALIGN=MIDDLE  ALT=\"15%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=225.  if so, you know that 169 would be between these numbers.  so it would either be 13 or 14  \r<BR>\n" );
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document.write( "Look at the ending...169 ends with a 9. <BR>\n" );
document.write( "if we multiply by 4*4, the ending number will be 6 AND we also know that when we multiply even numbers, the ending number will NEVER end with an odd number like 9.  \r<BR>\n" );
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document.write( "We know that when we multiply 3*3, it ends in 9. <BR>\n" );
document.write( "Then you know that 13*13 would be a good match. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%5E2 ALIGN=MIDDLE  ALT=\"13%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=169\r<BR>\n" );
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document.write( "You can try to memorize some or just take an educated guess when playing with numbers.<BR>\n" );
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