document.write( "Question 1126191: How many whole numbers are there, whose squares and cubes have the same number of digits? \n" ); document.write( "

Algebra.Com's Answer #742512 by ikleyn(52794) $\"\"$ $\"About$

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document.write( "It is clear even without my explanations that for n >= 10 the cube of n,  ,  has MORE digits than  the square  .\r\n" );
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document.write( "Therefore, only 1-digit numbers must be checked\r\n" );
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document.write( "n     n^2     n^3\r\n" );
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document.write( "0     0        0    (*)\r\n" );
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document.write( "1     1        1    (*)\r\n" );
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document.write( "2     4        8    (*)\r\n" );
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document.write( "3     9       27\r\n" );
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document.write( "4     16      64    (*)\r\n" );
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document.write( "5     25     125\r\n" );
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document.write( "6     36     256\r\n" );
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document.write( "7     49\r\n" );
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document.write( "8\r\n" );
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document.write( "9\r\n" );
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document.write( "For your convenience, I marked the favorable numbers by (*), so you can calculate the ANSWER on your own.\r\n" );
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