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Difficulty: MediumPuzzle Details

Puzzle IconWhich is larger:

the tenth root of 10, or the cube root of 2?

Show Hint Show Answer Print Puzzle
[Ref: ZHAI] © Kevin Stone 

Answer: Cube root of 2.

We have 101/10 vs 21/3.

Raise each to the power of 30 (since 10 x 3 = 30) to give:

101/10 x 30 vs 21/3 x 30, which simplifies to:

103 vs 210, which gives:

1000 vs 1024.

Therefore the cube root of 2 is larger. Alternatively we can use a calculator to see that the tenth root of 10 = 1.2589 and the cube root of 2 = 1.2599.


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