document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=124041>Question 124041</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Critical thinking\r<BR>\n" );
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document.write( "Suppose A is a whole number and B is an irrational number. Is it possible for the product of AB to be a rational number? Explain why or why not?\r<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 #90972 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=90972\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We are given A is a whole number and B is irrational.  Let's assume that the product A*B is rational.  That means that there are two integers p and q such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=p%2Fq ALIGN=MIDDLE  ALT=\"AB=p%2Fq\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Dividing both sides of the equation by A results in:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=p%2F%28Aq%29 ALIGN=MIDDLE  ALT=\"B=p%2F%28Aq%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "p was chosen as an integer, and since A is a whole number and q is an integer, Aq must be an integer.  Therefore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2F%28Aq%29 ALIGN=MIDDLE  ALT=\"p%2F%28Aq%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a rational number.\r<BR>\n" );
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document.write( "But that means B must be rational, contradicting the given condition that B be irrational.  Therefore the assumption that A*B is rational must be false and A*B must be irrational.\r<BR>\n" );
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