document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201492>Question 201492</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780495392767/algebrahomeworkh>precalculus</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> the square root of x minus 3 square root of x with an index of 4 minus 4 equals 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #151702 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=151702\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The easiest way to do this is based on understanding that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29+=+%28root%284%2C+x%29%29%5E2 ALIGN=MIDDLE  ALT=\"sqrt%28x%29+=+%28root%284%2C+x%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is not hard to see if you understand fractional exponents: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29+=+x%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29+=+x%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2C+x%29+=+x%5E%281%2F4%29 ALIGN=MIDDLE  ALT=\"root%284%2C+x%29+=+x%5E%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28root%284%2C+x%29%29%5E2+=+%28x%5E%281%2F4%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28root%284%2C+x%29%29%5E2+=+%28x%5E%281%2F4%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Using the appropriate rule for exposnents (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5Eb%29%5Ec+=+a%5E%28b%2Ac%29 ALIGN=MIDDLE  ALT=\"%28a%5Eb%29%5Ec+=+a%5E%28b%2Ac%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E%281%2F4%29%29%5E2+=+x%5E%28%281%2F4%29%2A2%29+=+x%5E%282%2F4%29+=+x%5E%281%2F2%29+=+sqrt%28x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "If we let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+root%284%2C+x%29 ALIGN=MIDDLE  ALT=\"y+=+root%284%2C+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=+sqrt%28x%29 ALIGN=MIDDLE  ALT=\"y%5E2+=+sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substituting these into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29+-3%2A%28root%284%2Cx%29%29+-4+=+0 ALIGN=MIDDLE  ALT=\"sqrt%28x%29+-3%2A%28root%284%2Cx%29%29+-4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+-+3y+-+4+=+0 ALIGN=MIDDLE  ALT=\"y%5E2+-+3y+-+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This equation can be easily solved by factoring:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+4%29%2A%28y+%2B+1%29+=+0 ALIGN=MIDDLE  ALT=\"%28y+-+4%29%2A%28y+%2B+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since a product of zero means one of the factors must be zero:<BR>\n" );
document.write( "y-4=0  or  y+1=0<BR>\n" );
document.write( "Adding 4 to both sides of the first equation and subtracting 1 from both sides of the second we get:<BR>\n" );
document.write( "y=4 or y=-1<BR>\n" );
document.write( "Now we substitute back in for y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2C+x%29+=+4 ALIGN=MIDDLE  ALT=\"root%284%2C+x%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2C+x%29+=+-1 ALIGN=MIDDLE  ALT=\"root%284%2C+x%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We reject the second equation because by definition <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2C+x%29 ALIGN=MIDDLE  ALT=\"root%284%2C+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > must not be negative. To solve the first equation we raise both sides to the 4th power:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28root%284%2C+x%29%29%5E4+=+4%5E4 ALIGN=MIDDLE  ALT=\"%28root%284%2C+x%29%29%5E4+=+4%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > which gives:<BR>\n" );
document.write( "x = 256\r<BR>\n" );
document.write( "\n" );
document.write( "Checking:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28256%29+-+3%2Aroot%284%2C+256%29+-+4+=+0 ALIGN=MIDDLE  ALT=\"sqrt%28256%29+-+3%2Aroot%284%2C+256%29+-+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "16 - 3*4 - 4 = 0<BR>\n" );
document.write( "16 - 12 - 4 = 0<BR>\n" );
document.write( "0 = 0 Check!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );