document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=44848>Question 44848</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am a whole number between 40,000 and 50,000.  When I am divided by 2, the asnwer is a perfect square.  When I am divided by 3, the answer is a perfect cube.  Who am I?\r<BR>\n" );
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document.write( "I need to explain how I got this\r<BR>\n" );
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document.write( "Help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #29722 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=29722\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am a whole number between 40,000 and 50,000. When I am divided by 2, the asnwer is a perfect square. When I am divided by 3, the answer is a perfect cube. Who am I? <BR>\n" );
document.write( "I need to explain how I got this <BR>\n" );
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document.write( "Let the number be #; then 40000<#<50000<BR>\n" );
document.write( "When # is divided by 3 the result is a perfect cube, as follows:<BR>\n" );
document.write( "#/3=y^3<BR>\n" );
document.write( "Then #=3y^3<BR>\n" );
document.write( "Put that into the inequality, as follows:<BR>\n" );
document.write( "40000<3y^3<50000<BR>\n" );
document.write( "Divide thru by 3 to get<BR>\n" );
document.write( "13333.333< y^3 <16666.666...\r<BR>\n" );
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document.write( "Take the cube root from left to right to get:<BR>\n" );
document.write( "23.7126...< y <25.5436...\r<BR>\n" );
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document.write( "Therefore y is either 24 or 25\r<BR>\n" );
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document.write( "Then #=3*24^3 or #=3*25^3\r<BR>\n" );
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document.write( "If #=3^24^3=41472<BR>\n" );
document.write( "When we divide this by 2 we get 20736<BR>\n" );
document.write( "If we take the square root we get 144.<BR>\n" );
document.write( "So when 41472 is divided by 2 we DO get a perfect square.<BR>\n" );
document.write( "And when we divide 41472 by 3 we DO get a perfect cube.\r<BR>\n" );
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document.write( "Could #=3*25^3 also be an acceptable answer?<BR>\n" );
document.write( "#=3*25^3= 46875<BR>\n" );
document.write( "When we divide by 2 we get 23437.5<BR>\n" );
document.write( "which is not a perfect square.\r<BR>\n" );
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document.write( "So the number you are looking for is 41472.\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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