document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=91198>Question 91198</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Prove that cube root of 7 is an IRRATIONAL number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66191 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=66191\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Prove that cube root of 7 is an IRRATIONAL number ?<BR>\n" );
document.write( "Assume that cube rt 7 is rational.<BR>\n" );
document.write( "Then (7)^(1/3) = a/b where a and b are integers and a/b is reduced to lowest terms.<BR>\n" );
document.write( "Then a=b[7^(1/3)]<BR>\n" );
document.write( "Since a is a multiple of b and a is an integer, b divides a.<BR>\n" );
document.write( "Since b divides a, a = nb and n is an integer.<BR>\n" );
document.write( "Therefore 7^(1/3) = a/b = nb/b, so a/b is not reduced to lowest terms.<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "What led to this contradiction?<BR>\n" );
document.write( "The assumption that 7^(1/3) was rational.<BR>\n" );
document.write( "The assumption must be wrong.<BR>\n" );
document.write( "Therefore 7^(1/3) if irrational.<BR>\n" );
document.write( "================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );