document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=91637>Question 91637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a problem on a take home test cube root of 125-xcubed =5-x do i first cube both sides to get rid of the radical or should i solve the radical on the left side  if i cube both sides i get 125- 5x to the 3 power.  if take the cube root of the left side i get 5i times square root of 5 =5-x  ihave no idea what to do please  help thank you very much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66555 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=66555\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> As I understand your problem it is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C125%29-x%5E3+=+5+-+x ALIGN=MIDDLE  ALT=\"root%283%2C125%29-x%5E3+=+5+-+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Recognize that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C125%29 ALIGN=MIDDLE  ALT=\"root%283%2C125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is just a number that you can get on a calculator.<BR>\n" );
document.write( "In this case, the answer can be done in your head. Ask yourself, \"What number multiplied<BR>\n" );
document.write( "by itself three times results in 125?\" It can't be 4*4*4 because that results in 64. How<BR>\n" );
document.write( "about 5*5*5. That answer is 125. (Note that -5*-5*-5 will not work because it results in<BR>\n" );
document.write( "minus 125.) So you can replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C125%29 ALIGN=MIDDLE  ALT=\"root%283%2C125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with 5. When you do that the problem<BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+-+x%5E3+=+5+-+x ALIGN=MIDDLE  ALT=\"5+-+x%5E3+=+5+-+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice that you have 5 on both sides of the equation. You can get rid of them by subtracting<BR>\n" );
document.write( "5 from both sides and the equation reduces to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E3+=+-x ALIGN=MIDDLE  ALT=\"-x%5E3+=+-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next add x^3 to both sides of the equation. When you do the -x^3 on the left side disappears<BR>\n" );
document.write( "and you are left with:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x%5E3+-+x ALIGN=MIDDLE  ALT=\"0+=+x%5E3+-+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let's transpose sides, just to make this into a little more familiar form:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-+x+=+0 ALIGN=MIDDLE  ALT=\"x%5E3+-+x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since both terms contain x, let's factor an x out and the problem becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%5E2+-1%29=+0 ALIGN=MIDDLE  ALT=\"x%28x%5E2+-1%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Then notice that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+1 ALIGN=MIDDLE  ALT=\"x%5E2+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the difference between two squares. This is in the standard<BR>\n" );
document.write( "factoring form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+-+b%5E2+=+%28a-b%29%2A%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"a%5E2+-+b%5E2+=+%28a-b%29%2A%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Applying this rule to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-1 ALIGN=MIDDLE  ALT=\"x%5E2+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > we find that<BR>\n" );
document.write( "it factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2A%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%2A%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we can put this into the equation in place of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-1 ALIGN=MIDDLE  ALT=\"x%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "With that substitution the equation we have becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-1%29%28x%2B1%29+=+0 ALIGN=MIDDLE  ALT=\"x%28x-1%29%28x%2B1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice that this equation will be true if any of the factors is equal to zero because<BR>\n" );
document.write( "multiplying by a zero on the left side will result in the equation becoming 0 = 0. So<BR>\n" );
document.write( "set each of the factors equal to zero and solve for x:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0 ALIGN=MIDDLE  ALT=\"x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <=== that's one answer<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+1+=+0+ ALIGN=MIDDLE  ALT=\"x+-+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve by adding 1 to both sides to get <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;\" > & that's another answer.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B1+=+0+ ALIGN=MIDDLE  ALT=\"x+%2B1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve by subtracting 1 from both sides to get <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;\" > & that's the last answer.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "In summary, the three answers are x = 0, x = +1, and x = -1. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can substitute these answers back into the original problem and see that they each <BR>\n" );
document.write( "work.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the problem. You didn't have to worry about the cube<BR>\n" );
document.write( "root because in this case it was just the number 5. If the cube root had involved a<BR>\n" );
document.write( "term containing x, that would have been a whole different problem.<BR>\n" );
document.write( ".<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );