??

Which is larger:

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

Puzzle Copyright © Kevin Stone

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Answer

Cube root of 2.

Reasoning

We could use a calculator to see that the tenth root of 10 = 1.2589 and the cube root of 2 = 1.2599.

But, if you've not got your calculator handy...

We have:

10^{1/10} vs 2^{1/3}

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

(10^{1/10})^{30} vs (2^{1/3})^{30}

10^{1/10 x 30} vs 2^{1/3 x 30}

10^{3} vs 2^{10}

1000 vs 1024

Therefore, the cube root of 2 is larger.

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