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Non-perfect Cube Root Sum (Posted on 2015-08-14) Difficulty: 3 of 5
Can the sum of two cube roots of positive non-perfect cubes be an integer?

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No Solution Yet Submitted by K Sengupta    
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solution | Comment 4 of 6 |
Since nothing was said about a and b being integers, take a=(x+y)^3 and b=(x-y)^3 where x is an integer and y is an irrational, say x=2 and y=2^1/2.  Then the sum of the cube roots of a and b is the integer 4.
  Posted by xdog on 2015-08-14 20:12:21
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