document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098844>Question 1098844</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
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document.write( "I would appreciate if someone might help here.\r<BR>\n" );
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document.write( "Exercise instructions: Express following in form X + Y*2^(1/2); X and Y are rational numbers:\r<BR>\n" );
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document.write( "       (7 + 5 * 2^(1/2))^(1/3) \r<BR>\n" );
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document.write( "The answer given is: 1 + 2^(1/2)\r<BR>\n" );
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document.write( "I have no idea how they got there.\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713242 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=713242\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If we are not given the solution, we just need to solve<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28X%2BY%2A2%5E%281%2F2%29%29%5E3=7%2B5%2A2%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28X%2BY%2A2%5E%281%2F2%29%29%5E3=7%2B5%2A2%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If you like square roots better than fractional exponents,<BR>\n" );
document.write( "feel free to write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%221+%2F+2%22 ALIGN=MIDDLE  ALT=\"2%5E%221+%2F+2%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <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;\" > .<BR>\n" );
document.write( "I will have to write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%221%2F2%22 ALIGN=MIDDLE  ALT=\"%221%2F2%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > in some places,<BR>\n" );
document.write( "to make sure that you see the whole fractional exponent,<BR>\n" );
document.write( "because I do not see the whole exponent in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"2%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E3%2B3%2AX%5E2%2AY%2A2%5E%281%2F2%29%2B3%2AX%2A%28Y%2A2%5E%281%2F2%29%29%5E2%2B%28Y%2A2%5E%281%2F2%29%29%5E3=7%2B5%2A2%5E%281%2F2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E3%2B3%2AX%5E2%2AY%2A2%5E%221+%2F+2%22%2B3%2AX%2AY%5E2%2A2%2BY%2A2%5E%223%2F2%22=7%2B5%2A2%5E%221%2F2%22 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E3%2B3%2AX%5E2%2AY%2A2%5E%221%2F2%22%2B6%2AX%2AY%5E2%2BY%2A2%2A2%5E%221%2F2%22=7%2B5%2A2%5E%221%2F2%22 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E3%2B6XY%5E2-7%2B%283X%5E2Y%2B2Y%5E3-5%29%2A2%5E%221%2F2%22=0 ALIGN=MIDDLE  ALT=\"X%5E3%2B6XY%5E2-7%2B%283X%5E2Y%2B2Y%5E3-5%29%2A2%5E%221%2F2%22=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we only need the one and only rational pair solution to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28X%5E3%2B6XY%5E2-7=0%2C3X%5E2%2B2Y%5E3-5=0%29 ALIGN=MIDDLE  ALT=\"system%28X%5E3%2B6XY%5E2-7=0%2C3X%5E2%2B2Y%5E3-5=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "When looking for rational solutions for polynomial equations,<BR>\n" );
document.write( "we just try numbers that look promising.<BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28X=1%2CY=1%29 ALIGN=MIDDLE  ALT=\"system%28X=1%2CY=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in those two equations,<BR>\n" );
document.write( "we find that they are a solution.<BR>\n" );
document.write( "Knowing that there was only one real solution to be found,<BR>\n" );
document.write( "we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28X=1%2CY=1%29 ALIGN=MIDDLE  ALT=\"system%28X=1%2CY=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives us<BR>\n" );
document.write( "THE one and only answer, which is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281%2B2%5E%221%2F2%22%29 ALIGN=MIDDLE  ALT=\"highlight%281%2B2%5E%221%2F2%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , also known as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsqrt%282%29 ALIGN=MIDDLE  ALT=\"1%2Bsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE: If the question was stated as \"prove that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2B5%2A2%5E%281%2F2%29%29%5E%281%2F3%29+=1%2B2%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%287%2B5%2A2%5E%281%2F2%29%29%5E%281%2F3%29+=1%2B2%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,\" all we would have needed to do is calculate<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B2%5E%221%2F2%22%29%5E3 ALIGN=MIDDLE  ALT=\"%281%2B2%5E%221%2F2%22%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , by expanding that cube of a binomial,<BR>\n" );
document.write( "and simplifying as needed.<BR>\n" );
document.write( "As asked, the problem was not as difficult as it was intimidating,<BR>\n" );
document.write( "encouraging you to give up. </SPAN>\n" );
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