document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=114337>Question 114337</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I still don't get this square root thing - can someone please explain?\r<BR>\n" );
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document.write( "Solve using the square root property:\r<BR>\n" );
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document.write( "(x+8)^2 = 81 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83203 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=83203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A square root of a number is another number, when multiplied by itself results in the original number.  2 is a square root of 4, for example.  The thing is, whenever you take a square root, you need to consider both the positive and the negative, because -2 is also a square root of 4.\r<BR>\n" );
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document.write( "So let's look at your problem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B8%29%5E2=81 ALIGN=MIDDLE  ALT=\"%28x%2B8%29%5E2=81\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The first thing you need to do is take the square root of both sides of the equation.  Beginning with the left side of the equation, remember that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2%29=a ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2%29=a\"   DISABLED_style= \"max-width:90%; height:auto;\" > for any real number a.  On the right side of the equation, ask yourself, what number when multiplied by itself equals 81?  I sincerely hope you came up with both 9 and -9.\r<BR>\n" );
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document.write( "So now we can re-write the equation like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x%2B8%29%5E2%29=sqrt%2881%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x%2B8%29%5E2%29=sqrt%2881%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x%2B8%29%5E2%29=-sqrt%2881%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x%2B8%29%5E2%29=-sqrt%2881%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B8=9 ALIGN=MIDDLE  ALT=\"x%2B8=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B8=-9 ALIGN=MIDDLE  ALT=\"x%2B8=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-17 ALIGN=MIDDLE  ALT=\"x=-17\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's check to see if the answers make the original statement true:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B8%29%5E2=81 ALIGN=MIDDLE  ALT=\"%281%2B8%29%5E2=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <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;\" >, so that answer checks<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-17%2B8%29%5E2=81 ALIGN=MIDDLE  ALT=\"%28-17%2B8%29%5E2=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-9%29%5E2=81 ALIGN=MIDDLE  ALT=\"%28-9%29%5E2=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > so that answer checks as well.\r<BR>\n" );
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document.write( "If you are confused at all about the fact that there are two answers, don't worry.  Having two answers for a 2nd-degree equation (one that has an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy ALIGN=MIDDLE  ALT=\"xy\"   DISABLED_style= \"max-width:90%; height:auto;\" > term in it) is part of the great and wonderful pattern of mathematics.  You'll discover later on that 3rd-degree equations, such as things with an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > in them will have THREE solutions or roots.  In fact, the fundamental theorem of algebra tells us that an n-th degree equation has n roots.  For the time being, have faith.  It will all make good sense in the end.\r<BR>\n" );
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document.write( "Hope that helps,<BR>\n" );
document.write( "John </SPAN>\n" );
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