document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=128032>Question 128032</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618073949/algebrahomeworkh>integrated mathematics 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> i dont get the whole chapter... of 9-2. the square roots and everything. like #16, it says 2x^2=36...i dont get that </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93755 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=93755\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Squaring a number is multiplying it by itself.  2 squared is 2 X 2 is 4, for example.  The square root is just the opposite of that.  If I want the square root of a number, find a number when multiplied by itself gives the original number.  So if I want the square root of 9, I know that 3 X 3 is 9, so 3 is the square root of 9.  But 3 is only one of the square roots of 9, because -3 X -3 is also 9.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "As for notation, if you see <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29 ALIGN=MIDDLE  ALT=\"sqrt%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then by convention, the positive square root is meant.  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29=3 ALIGN=MIDDLE  ALT=\"sqrt%289%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a true statement.  But if the problem is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=9 ALIGN=MIDDLE  ALT=\"x%5E2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you must consider both the positive and negative values for x that would make the statement true.  In this case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's look at your example problem:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2=36 ALIGN=MIDDLE  ALT=\"2x%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "First step is to divide both sides by 2:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=18 ALIGN=MIDDLE  ALT=\"x%5E2=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now we can take the square root of both sides of the equation:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%2818%29 ALIGN=MIDDLE  ALT=\"x=sqrt%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-sqrt%2818%29 ALIGN=MIDDLE  ALT=\"x=-sqrt%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "But we aren't quite done yet.  One of the rules for square roots says:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28ab%29=sqrt%28a%29%2Asqrt%28b%29 ALIGN=MIDDLE  ALT=\"sqrt%28ab%29=sqrt%28a%29%2Asqrt%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18=2%2A9 ALIGN=MIDDLE  ALT=\"18=2%2A9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we can write our earlier answer as:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%289%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"x=sqrt%289%29%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-sqrt%289%29sqrt%282%29 ALIGN=MIDDLE  ALT=\"x=-sqrt%289%29sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but remember <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29=3 ALIGN=MIDDLE  ALT=\"sqrt%289%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the final result is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"x=3%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"x=-3%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That's as far as you can go without making an approximation since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is irrational, meaning that it cannot be expressed exactly as a decimal.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );