document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=957853>Question 957853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how to solve= 1/cube root 4+ cube root 2 +1\r<BR>\n" );
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document.write( "i know the ans is cube root 2 -1 but i dont know how to solve it<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 #585378 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=585378\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First of all, please put multiple-term numerators and denominators in parentheses. What you posted meant:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Froot%283%2C+4%29+%2B+root%283%2C+2%29+%2B+1 ALIGN=MIDDLE  ALT=\"1%2Froot%283%2C+4%29+%2B+root%283%2C+2%29+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "But I'm quite sure you meant:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28root%283%2C+4%29+%2B+root%283%2C+2%29+%2B+1%29 ALIGN=MIDDLE  ALT=\"1%2F%28root%283%2C+4%29+%2B+root%283%2C+2%29+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which should be posted as:<BR>\n" );
document.write( "1/(cube root 4+ cube root 2 +1)<BR>\n" );
document.write( "Tutors are more likely to respond if problems are posted clearly.<br><BR>\n" );
document.write( "Clearing cube roots from a multiple-term denominator involves use of one or both of the following patterns:<ul><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3%2Bb%5E3+=+%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"a%5E3%2Bb%5E3+=+%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3-b%5E3+=+%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"a%5E3-b%5E3+=+%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li></ul>A relatively fast way to simplify this requires that we recognizing that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+4%29+=+%28root%283%2C+2%29%29%5E2 ALIGN=MIDDLE  ALT=\"root%283%2C+4%29+=+%28root%283%2C+2%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substituting this into our expression we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%28root%283%2C+2%29%29%5E2+%2B+root%283%2C+2%29+%2B+1%29 ALIGN=MIDDLE  ALT=\"1%2F%28%28root%283%2C+2%29%29%5E2+%2B+root%283%2C+2%29+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we need to recognize that this denominator matches the pattern of the second factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3-b%5E3+=+%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"a%5E3-b%5E3+=+%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with an \"a\" of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+2%29 ALIGN=MIDDLE  ALT=\"root%283%2C+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a \"b\" of 1. The pattern shows us that if we multiply that factor by (a-b) then we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3-b%5E3 ALIGN=MIDDLE  ALT=\"a%5E3-b%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. With all terms being perfect cubes, this will eliminate the cube roots.<br><BR>\n" );
document.write( "So we multiply the numerator and denominator by (a-b) with an \"a\" of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+2%29 ALIGN=MIDDLE  ALT=\"root%283%2C+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a \"b\" of 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28%28root%283%2C+2%29%29%5E2+%2B+root%283%2C+2%29+%2B+1%29%29%28%28root%283%2C+2%29+-+1%29%2F%28root%283%2C+2%29+-+1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In the denominator, the pattern tells us what we get. In the numerator we just use the Distributive Property:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28root%283%2C+2%29+-+1%29%2F%28%28root%283%2C+2%29%29%5E3+-+%281%29%5E3%29%29 ALIGN=MIDDLE  ALT=\"%28root%283%2C+2%29+-+1%29%2F%28%28root%283%2C+2%29%29%5E3+-+%281%29%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28root%283%2C+2%29+-+1%29%2F%282-1%29 ALIGN=MIDDLE  ALT=\"%28root%283%2C+2%29+-+1%29%2F%282-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28root%283%2C+2%29+-+1%29%2F1 ALIGN=MIDDLE  ALT=\"%28root%283%2C+2%29+-+1%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+2%29+-+1 ALIGN=MIDDLE  ALT=\"root%283%2C+2%29+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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