document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=256349>Question 256349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HELP PLEASE!! <BR>\n" );
document.write( "Give an example of two irrational numbers whose product is an irrational number. AND Give an example of two irrational numbers whose product is a rational number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188467 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=188467\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1 Give an example of two irrational numbers whose product is an irrational number.\r<BR>\n" );
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document.write( "The numbers <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are both irrational and so is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2Asqrt%283%29=sqrt%282%2A3%29=sqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2Asqrt%283%29=sqrt%282%2A3%29=sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the product of <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (both irrational) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is also irrational).\r<BR>\n" );
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document.write( "# 2  Give an example of two irrational numbers whose product is a rational number\r<BR>\n" );
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document.write( "The numbers <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288%29 ALIGN=MIDDLE  ALT=\"sqrt%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are irrational, but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2Asqrt%288%29=sqrt%282%2A8%29=sqrt%2816%29=4 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2Asqrt%288%29=sqrt%282%2A8%29=sqrt%2816%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is clearly rational.\r<BR>\n" );
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document.write( "So the product of <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288%29 ALIGN=MIDDLE  ALT=\"sqrt%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (both irrational) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is rational). </SPAN>\n" );
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