document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=465887>Question 465887</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am supposed to solve this:<BR>\n" );
document.write( "3+ root symbol (z-8) = root symbol(z+7)\r<BR>\n" );
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document.write( "I am not sure what to do here, any help would be appreciated! With explanation if possible! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #319272 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=319272\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Bsqrt%28z-8%29=+sqrt%28z%2B7%29 ALIGN=MIDDLE  ALT=\"3%2Bsqrt%28z-8%29=+sqrt%28z%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The next step is to square both sides. Squaring the left side is done by multiplying:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Bsqrt%28z-8%29%29%2A%283%2Bsqrt%28z-8%29%29 ALIGN=MIDDLE  ALT=\"%283%2Bsqrt%28z-8%29%29%2A%283%2Bsqrt%28z-8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This can be done by using the FOIL method ... multiply First Terms, then Outside Terms, then Inside Terms, and finally Last Terms.  When you do that you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A3%29%2B3%2Asqrt%28z-8%29+%2B3%2Asqrt%28z-8%29%2Bsqrt%28z-8%29%2Asqrt%28z-8%29 ALIGN=MIDDLE  ALT=\"%283%2A3%29%2B3%2Asqrt%28z-8%29+%2B3%2Asqrt%28z-8%29%2Bsqrt%28z-8%29%2Asqrt%28z-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+%2B+6%2Asqrt%28z-8%29%2B%28z-8%29 ALIGN=MIDDLE  ALT=\"9+%2B+6%2Asqrt%28z-8%29%2B%28z-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which further simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+%2B+6%2Asqrt%28z-8%29%2Bz+-8 ALIGN=MIDDLE  ALT=\"9+%2B+6%2Asqrt%28z-8%29%2Bz+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "and the +9 and -8 combines to +1 so the expression reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%28z-8%29+%2Bz+%2B+1 ALIGN=MIDDLE  ALT=\"6%2Asqrt%28z-8%29+%2Bz+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now return to square the right side of the equation as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28z%2B7%29%2Asqrt%28z%2B7%29+=+z%2B7 ALIGN=MIDDLE  ALT=\"sqrt%28z%2B7%29%2Asqrt%28z%2B7%29+=+z%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So after squaring both sides the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%28z-8%29+%2B+z+%2B+1+=+z+%2B+7 ALIGN=MIDDLE  ALT=\"6%2Asqrt%28z-8%29+%2B+z+%2B+1+=+z+%2B+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract z from both sides reduces this to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%28z-8%29+%2B+1+=+7 ALIGN=MIDDLE  ALT=\"6%2Asqrt%28z-8%29+%2B+1+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next subtract 1 from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%28z-8%29+=+6 ALIGN=MIDDLE  ALT=\"6%2Asqrt%28z-8%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides by 6:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28z-8%29+=+1 ALIGN=MIDDLE  ALT=\"sqrt%28z-8%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Square both sides:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z-8+=+1 ALIGN=MIDDLE  ALT=\"z-8+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally add 8 to both sides and the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+9 ALIGN=MIDDLE  ALT=\"z+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That's the answer. You can check this by returning to the original equation, substituting 9 for z, and working it out to see that both sides are equal.  In other words, start with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Bsqrt%28z-8%29=+sqrt%28z%2B7%29 ALIGN=MIDDLE  ALT=\"3%2Bsqrt%28z-8%29=+sqrt%28z%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute 9 for z:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+sqrt%289-8%29=sqrt%289%2B7%29 ALIGN=MIDDLE  ALT=\"3+%2B+sqrt%289-8%29=sqrt%289%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine the numbers under each radical to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+sqrt%281%29=sqrt%2816%29 ALIGN=MIDDLE  ALT=\"3+%2B+sqrt%281%29=sqrt%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+1+=+4 ALIGN=MIDDLE  ALT=\"3+%2B+1+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And this is true (4 does equal 4) so our answer of z = 9 does satisfy the original equation.<BR>\n" );
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document.write( "Hope this helps you to understand that squaring radicals is a way to solve problems such as these.<BR>\n" );
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