document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252285>Question 252285</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many numbers from 1 to 1 million, inclusive, are NOT perfect squares or perfect cubes?\r<BR>\n" );
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document.write( "a. 998,000 b. 998,830 c. 998,900 d. 998,910 e. 999,000 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184165 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=184165\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First lets look at perfect squares: 1^2, 2^2, 3^2, 4^2, . . . , 1000^2 are all perfect squares <= 1 million, inclusive.\r<BR>\n" );
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document.write( "Second, let's look at perfect cubes: 1^3, 2^3, 3^3, 4^3, . . . , 100^3 are all perfect cubes less than or equal to 1 million inclusive.\r<BR>\n" );
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document.write( "So we have 1100 so far. \r<BR>\n" );
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document.write( "But notice that some perfect squares are perfect cubes. That occurs at perfect sixth powers. we have to eliminate this overlap. Perfect sixth powers are: 1^6, 2^6, 3^6, . . . , 10^6 are all perfect sixth powers less than or equal to 1 million inclusive.\r<BR>\n" );
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document.write( "So, 1 million - 1100 +10 = 998,910. </SPAN>\n" );
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