document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=307270>Question 307270</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If (y -3)^2 = 16, what is the smallest possible value of y^2?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #219843 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=219843\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (y-3)^2 = 16\r<BR>\n" );
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document.write( "Take square root of both sides of the equation to get:\r<BR>\n" );
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document.write( "y-3 = 4\r<BR>\n" );
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document.write( "Add 3 to both sides of the equation to get:\r<BR>\n" );
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document.write( "y = 7\r<BR>\n" );
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document.write( "The only value that y can be is 7.\r<BR>\n" );
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document.write( "There is no other value of y that would satisfy this equation which is why I wonder why you asked for the smallest value of y.\r<BR>\n" );
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document.write( "Substitute for 7 in the original equation to get:\r<BR>\n" );
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document.write( "(7-3)^2 = 16 which becomes:\r<BR>\n" );
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document.write( "4^2 = 16 which becomes:\r<BR>\n" );
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document.write( "16 = 16 which is true, confirming that y = 7 is the correct value to satisfy the equation.\r<BR>\n" );
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document.write( "If this was an inequality, such as:\r<BR>\n" );
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document.write( "(y-3)^2 >= 16, then you might ask for the smallest value of y.\r<BR>\n" );
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document.write( "You would solve the inequality pretty much the way you would solve the equality.\r<BR>\n" );
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document.write( "Take the square root of both sides of this equation to get:\r<BR>\n" );
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document.write( "y-3 >= 4\r<BR>\n" );
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document.write( "Add 3 to both sides of this equation to get:\r<BR>\n" );
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document.write( "y >= 7\r<BR>\n" );
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document.write( "The smallest value y could be then would be 7.\r<BR>\n" );
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document.write( "If you had the inequality equation of:\r<BR>\n" );
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document.write( "(y-3)^2 > 16, then you would solve again using the same method.\r<BR>\n" );
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document.write( "Take the square root of both sides of the equation to getr:\r<BR>\n" );
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document.write( "y-3 > 4\r<BR>\n" );
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document.write( "Add 3 to both sides of the equation to get y > 7\r<BR>\n" );
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document.write( "then the smallest value that y could be would be something greater than 7.\r<BR>\n" );
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document.write( "If you were looking for integers, it would be 8.\r<BR>\n" );
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document.write( "If you allowed real numbers than it could be anything as long as it was grater than 7.\r<BR>\n" );
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document.write( "7.01, 7.001, 7.0001, 7.000001, etc.\r<BR>\n" );
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