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A square is a cube (Posted on 2012-11-29) Difficulty: 1 of 5
What 2-digit number(s), when squared, produces a number equal to the cube of its sum of digits?

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

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Solution A simpler way (spoiler) Comment 2 of 2 |
If a number when squared is a cube, then the original number is also a cube.

The only two digit cubes are 27 and 64.

The cube root of 27 = 3, squared = 9 = 2 + 7, so 27 works.
The cube root of 64 = 4, squared = 16 <> 6 + 4,

So 27 is the only answer.


  Posted by Steve Herman on 2012-11-29 13:21:39
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